diff --git a/sklearn/manifold/_spectral_embedding.py b/sklearn/manifold/_spectral_embedding.py
index b43329a4f89ca..13181a653d1dc 100644
--- a/sklearn/manifold/_spectral_embedding.py
+++ b/sklearn/manifold/_spectral_embedding.py
@@ -5,6 +5,7 @@
 # License: BSD 3 clause
 
 
+from numbers import Integral, Real
 import warnings
 
 import numpy as np
@@ -22,6 +23,7 @@
 )
 from ..utils._arpack import _init_arpack_v0
 from ..utils.extmath import _deterministic_vector_sign_flip
+from ..utils._param_validation import Interval, StrOptions
 from ..utils.fixes import lobpcg
 from ..metrics.pairwise import rbf_kernel
 from ..neighbors import kneighbors_graph, NearestNeighbors
@@ -542,6 +544,27 @@ class SpectralEmbedding(BaseEstimator):
     (100, 2)
     """
 
+    _parameter_constraints: dict = {
+        "n_components": [Interval(Integral, 1, None, closed="left")],
+        "affinity": [
+            StrOptions(
+                {
+                    "nearest_neighbors",
+                    "rbf",
+                    "precomputed",
+                    "precomputed_nearest_neighbors",
+                },
+            ),
+            callable,
+        ],
+        "gamma": [Interval(Real, 0, None, closed="left"), None],
+        "random_state": ["random_state"],
+        "eigen_solver": [StrOptions({"arpack", "lobpcg", "amg"}), None],
+        "eigen_tol": [Interval(Real, 0, None, closed="left"), StrOptions({"auto"})],
+        "n_neighbors": [Interval(Integral, 1, None, closed="left"), None],
+        "n_jobs": [None, Integral],
+    }
+
     def __init__(
         self,
         n_components=2,
@@ -649,28 +672,11 @@ def fit(self, X, y=None):
         self : object
             Returns the instance itself.
         """
+        self._validate_params()
 
         X = self._validate_data(X, accept_sparse="csr", ensure_min_samples=2)
 
         random_state = check_random_state(self.random_state)
-        if isinstance(self.affinity, str):
-            if self.affinity not in {
-                "nearest_neighbors",
-                "rbf",
-                "precomputed",
-                "precomputed_nearest_neighbors",
-            }:
-                raise ValueError(
-                    "%s is not a valid affinity. Expected "
-                    "'precomputed', 'rbf', 'nearest_neighbors' "
-                    "or a callable."
-                    % self.affinity
-                )
-        elif not callable(self.affinity):
-            raise ValueError(
-                "'affinity' is expected to be an affinity name or a callable. Got: %s"
-                % self.affinity
-            )
 
         affinity_matrix = self._get_affinity_matrix(X)
         self.embedding_ = spectral_embedding(
diff --git a/sklearn/manifold/tests/test_spectral_embedding.py b/sklearn/manifold/tests/test_spectral_embedding.py
index 37412eac14490..cf7f253b66de1 100644
--- a/sklearn/manifold/tests/test_spectral_embedding.py
+++ b/sklearn/manifold/tests/test_spectral_embedding.py
@@ -351,17 +351,6 @@ def test_spectral_embedding_unknown_eigensolver(seed=36):
         se.fit(S)
 
 
-def test_spectral_embedding_unknown_affinity(seed=36):
-    # Test that SpectralClustering fails with an unknown affinity type
-    se = SpectralEmbedding(
-        n_components=1,
-        affinity="<unknown>",
-        random_state=np.random.RandomState(seed),
-    )
-    with pytest.raises(ValueError):
-        se.fit(S)
-
-
 def test_connectivity(seed=36):
     # Test that graph connectivity test works as expected
     graph = np.array(
diff --git a/sklearn/tests/test_common.py b/sklearn/tests/test_common.py
index f0ee188c431a9..b4b41f5c88254 100644
--- a/sklearn/tests/test_common.py
+++ b/sklearn/tests/test_common.py
@@ -485,7 +485,6 @@ def test_estimators_do_not_raise_errors_in_init_or_set_params(Estimator):
     "SelectFromModel",
     "SpectralBiclustering",
     "SpectralCoclustering",
-    "SpectralEmbedding",
 ]