diff --git a/doc/developers/develop.rst b/doc/developers/develop.rst
index f17c58cee0d7f..13d2010ca7319 100644
--- a/doc/developers/develop.rst
+++ b/doc/developers/develop.rst
@@ -246,13 +246,13 @@ whether it is just for you or for contributing it to scikit-learn, there are
 several internals of scikit-learn that you should be aware of in addition to
 the scikit-learn API outlined above. You can check whether your estimator
 adheres to the scikit-learn interface and standards by running
-:func:`utils.estimator_checks.check_estimator` on the class or using
-:func:`~sklearn.utils.parametrize_with_checks` pytest decorator (see its
-docstring for details and possible interactions with `pytest`)::
+:func:`~sklearn.utils.estimator_checks.check_estimator` on an instance. The
+:func:`~sklearn.utils.parametrize_with_checks` pytest decorator can also be
+used (see its docstring for details and possible interactions with `pytest`)::
 
   >>> from sklearn.utils.estimator_checks import check_estimator
   >>> from sklearn.svm import LinearSVC
-  >>> check_estimator(LinearSVC)  # passes
+  >>> check_estimator(LinearSVC())  # passes
 
 The main motivation to make a class compatible to the scikit-learn estimator
 interface might be that you want to use it together with model evaluation and
diff --git a/doc/whats_new/v0.23.rst b/doc/whats_new/v0.23.rst
index 4357845885e3f..f9b8e25176265 100644
--- a/doc/whats_new/v0.23.rst
+++ b/doc/whats_new/v0.23.rst
@@ -511,6 +511,11 @@ Changelog
   matrix from a pandas DataFrame that contains only `SparseArray`s.
   :pr:`16728` by `Thomas Fan`_.
 
+- |API| Passing classes to :func:`utils.estimator_checks.check_estimator` and
+  :func:`utils.estimator_checks.parametrize_with_checks` is now deprecated,
+  and support for classes will be removed in 0.24. Pass instances instead.
+  :pr:`17032` by `Nicolas Hug`_.
+
 :mod:`sklearn.cluster`
 ......................
 
diff --git a/sklearn/tests/test_common.py b/sklearn/tests/test_common.py
index af98c1bc50a74..73c99b0483de8 100644
--- a/sklearn/tests/test_common.py
+++ b/sklearn/tests/test_common.py
@@ -48,7 +48,9 @@ def test_all_estimator_no_base_class():
         assert not name.lower().startswith('base'), msg
 
 
+@ignore_warnings("Passing a class is depr", category=FutureWarning)  # 0.24
 def test_estimator_cls_parameterize_with_checks():
+    # TODO: remove test in 0.24
     # Non-regression test for #16707 to ensure that parametrize_with_checks
     # works with estimator classes
     param_checks = parametrize_with_checks([LogisticRegression])
@@ -105,7 +107,7 @@ def _tested_estimators():
         yield estimator
 
 
-@parametrize_with_checks(_tested_estimators())
+@parametrize_with_checks(list(_tested_estimators()))
 def test_estimators(estimator, check, request):
     # Common tests for estimator instances
     with ignore_warnings(category=(FutureWarning,
@@ -115,7 +117,9 @@ def test_estimators(estimator, check, request):
         check(estimator)
 
 
+@ignore_warnings("Passing a class is depr", category=FutureWarning)  # 0.24
 def test_check_estimator_generate_only():
+    # TODO in 0.24: remove checks on passing a class
     estimator_cls_gen_checks = check_estimator(LogisticRegression,
                                                generate_only=True)
     all_instance_gen_checks = check_estimator(LogisticRegression(),
@@ -238,3 +242,19 @@ def test_all_tests_are_importable():
                                  '__init__.py or an add_subpackage directive '
                                  'in the parent '
                                  'setup.py'.format(missing_tests))
+
+
+# TODO: remove in 0.24
+def test_class_support_deprecated():
+    # Make sure passing classes to check_estimator or parametrize_with_checks
+    # is deprecated
+
+    msg = "Passing a class is deprecated"
+    with pytest.warns(FutureWarning, match=msg):
+        check_estimator(LogisticRegression)
+
+    with pytest.warns(FutureWarning, match=msg):
+        parametrize_with_checks([LogisticRegression])
+
+    # Make sure check_parameters_default_constructible accepts instances now
+    check_parameters_default_constructible('name', LogisticRegression())
diff --git a/sklearn/utils/estimator_checks.py b/sklearn/utils/estimator_checks.py
index efac2aca2a2df..ec28cb22919f0 100644
--- a/sklearn/utils/estimator_checks.py
+++ b/sklearn/utils/estimator_checks.py
@@ -33,7 +33,7 @@
 from ..linear_model import Ridge
 
 from ..base import (clone, ClusterMixin, is_classifier, is_regressor,
-                    RegressorMixin, is_outlier_detector)
+                    RegressorMixin, is_outlier_detector, BaseEstimator)
 
 from ..metrics import accuracy_score, adjusted_rand_score, f1_score
 from ..random_projection import BaseRandomProjection
@@ -333,12 +333,15 @@ def _construct_instance(Estimator):
     return estimator
 
 
+# TODO: probably not needed anymore in 0.24 since _generate_class_checks should
+# be removed too. Just put this in check_estimator()
 def _generate_instance_checks(name, estimator):
     """Generate instance checks."""
     yield from ((estimator, partial(check, name))
                 for check in _yield_all_checks(name, estimator))
 
 
+# TODO: remove this in 0.24
 def _generate_class_checks(Estimator):
     """Generate class checks."""
     name = Estimator.__name__
@@ -353,6 +356,8 @@ def _mark_xfail_checks(estimator, check, pytest):
     if isinstance(estimator, type):
         # try to construct estimator instance, if it is unable to then
         # return the estimator class, ignoring the tag
+        # TODO: remove this if block in 0.24 since passing instances isn't
+        # supported anymore
         try:
             estimator = _construct_instance(estimator)
         except Exception:
@@ -385,6 +390,10 @@ def parametrize_with_checks(estimators):
     estimators : list of estimators objects or classes
         Estimators to generated checks for.
 
+        .. deprecated:: 0.23
+           Passing a class is deprecated from version 0.23, and won't be
+           supported in 0.24. Pass an instance instead.
+
     Returns
     -------
     decorator : `pytest.mark.parametrize`
@@ -395,13 +404,21 @@ def parametrize_with_checks(estimators):
     >>> from sklearn.linear_model import LogisticRegression
     >>> from sklearn.tree import DecisionTreeRegressor
 
-    >>> @parametrize_with_checks([LogisticRegression, DecisionTreeRegressor])
+    >>> @parametrize_with_checks([LogisticRegression(),
+    ...                           DecisionTreeRegressor()])
     ... def test_sklearn_compatible_estimator(estimator, check):
     ...     check(estimator)
 
     """
     import pytest
 
+    if any(isinstance(est, type) for est in estimators):
+        # TODO: remove class support in 0.24 and update docstrings
+        msg = ("Passing a class is deprecated since version 0.23 "
+               "and won't be supported in 0.24."
+               "Please pass an instance instead.")
+        warnings.warn(msg, FutureWarning)
+
     checks_generator = chain.from_iterable(
         check_estimator(estimator, generate_only=True)
         for estimator in estimators)
@@ -418,7 +435,7 @@ def check_estimator(Estimator, generate_only=False):
     """Check if estimator adheres to scikit-learn conventions.
 
     This estimator will run an extensive test-suite for input validation,
-    shapes, etc, making sure that the estimator complies with `scikit-leanrn`
+    shapes, etc, making sure that the estimator complies with `scikit-learn`
     conventions as detailed in :ref:`rolling_your_own_estimator`.
     Additional tests for classifiers, regressors, clustering or transformers
     will be run if the Estimator class inherits from the corresponding mixin
@@ -426,7 +443,9 @@ def check_estimator(Estimator, generate_only=False):
 
     This test can be applied to classes or instances.
     Classes currently have some additional tests that related to construction,
-    while passing instances allows the testing of multiple options.
+    while passing instances allows the testing of multiple options. However,
+    support for classes is deprecated since version 0.23 and will be removed
+    in version 0.24 (class checks will still be run on the instances).
 
     Setting `generate_only=True` returns a generator that yields (estimator,
     check) tuples where the check can be called independently from each
@@ -439,9 +458,13 @@ def check_estimator(Estimator, generate_only=False):
 
     Parameters
     ----------
-    estimator : estimator object or class
+    estimator : estimator object
         Estimator to check. Estimator is a class object or instance.
 
+        .. deprecated:: 0.23
+           Passing a class is deprecated from version 0.23, and won't be
+           supported in 0.24. Pass an instance instead.
+
     generate_only : bool, optional (default=False)
         When `False`, checks are evaluated when `check_estimator` is called.
         When `True`, `check_estimator` returns a generator that yields
@@ -456,8 +479,14 @@ def check_estimator(Estimator, generate_only=False):
         Generator that yields (estimator, check) tuples. Returned when
         `generate_only=True`.
     """
+    # TODO: remove class support in 0.24 and update docstrings
     if isinstance(Estimator, type):
         # got a class
+        msg = ("Passing a class is deprecated since version 0.23 "
+               "and won't be supported in 0.24."
+               "Please pass an instance instead.")
+        warnings.warn(msg, FutureWarning)
+
         checks_generator = _generate_class_checks(Estimator)
     else:
         # got an instance
@@ -2570,6 +2599,12 @@ def check_parameters_default_constructible(name, Estimator):
     # this check works on classes, not instances
     # test default-constructibility
     # get rid of deprecation warnings
+    if isinstance(Estimator, BaseEstimator):
+        # Convert estimator instance to its class
+        # TODO: Always convert to class in 0.24, because check_estimator() will
+        # only accept instances, not classes
+        Estimator = Estimator.__class__
+
     with ignore_warnings(category=FutureWarning):
         estimator = _construct_instance(Estimator)
         # test cloning
diff --git a/sklearn/utils/tests/test_estimator_checks.py b/sklearn/utils/tests/test_estimator_checks.py
index a755daa842ef5..594ff65f9e889 100644
--- a/sklearn/utils/tests/test_estimator_checks.py
+++ b/sklearn/utils/tests/test_estimator_checks.py
@@ -356,6 +356,7 @@ def fit(self, X, y):
     check_fit_score_takes_y("test", TestEstimatorWithDeprecatedFitMethod())
 
 
+@ignore_warnings("Passing a class is depr", category=FutureWarning)  # 0.24
 def test_check_estimator():
     # tests that the estimator actually fails on "bad" estimators.
     # not a complete test of all checks, which are very extensive.
@@ -579,7 +580,10 @@ def test_check_regressor_data_not_an_array():
                         EstimatorInconsistentForPandas())
 
 
+@ignore_warnings("Passing a class is depr", category=FutureWarning)  # 0.24
 def test_check_estimator_required_parameters_skip():
+    # TODO: remove whole test in 0.24 since passes classes to check_estimator()
+    # isn't supported anymore
     class MyEstimator(BaseEstimator):
         _required_parameters = ["special_parameter"]