diff --git a/doc/whats_new/upcoming_changes/sklearn.preprocessing/29307.enhancement.rst b/doc/whats_new/upcoming_changes/sklearn.preprocessing/29307.enhancement.rst
new file mode 100644
index 0000000000000..55fd869902d62
--- /dev/null
+++ b/doc/whats_new/upcoming_changes/sklearn.preprocessing/29307.enhancement.rst
@@ -0,0 +1,4 @@
+- The :class:`preprocessing.PowerTransformer` now returns a warning 
+  when NaN values are encountered in the inverse transform, `inverse_transform`, typically 
+  caused by extremely skewed data.
+  By :user:Roberto Mourao <maf-rnmourao>
\ No newline at end of file
diff --git a/sklearn/preprocessing/_data.py b/sklearn/preprocessing/_data.py
index 99f7ac486e545..3213dccab5a8f 100644
--- a/sklearn/preprocessing/_data.py
+++ b/sklearn/preprocessing/_data.py
@@ -3501,9 +3501,21 @@ def inverse_transform(self, X):
             "yeo-johnson": self._yeo_johnson_inverse_transform,
         }[self.method]
         for i, lmbda in enumerate(self.lambdas_):
-            with np.errstate(invalid="ignore"):  # hide NaN warnings
-                X[:, i] = inv_fun(X[:, i], lmbda)
-
+            with warnings.catch_warnings(record=True) as captured_warnings:
+                with np.errstate(invalid="warn"):
+                    X[:, i] = inv_fun(X[:, i], lmbda)
+            if any(
+                "invalid value encountered in power" in str(w.message)
+                for w in captured_warnings
+            ):
+                warnings.warn(
+                    f"Some values in column {i} of the inverse-transformed data "
+                    f"are NaN. This may be caused by numerical issues in the "
+                    f"transformation process, e.g. extremely skewed data. "
+                    f"Consider inspecting the input data or preprocessing it "
+                    f"before applying the transformation.",
+                    UserWarning,
+                )
         return X
 
     def _yeo_johnson_inverse_transform(self, x, lmbda):
diff --git a/sklearn/preprocessing/tests/test_data.py b/sklearn/preprocessing/tests/test_data.py
index 60a3af0d02d61..62edb701b3bcc 100644
--- a/sklearn/preprocessing/tests/test_data.py
+++ b/sklearn/preprocessing/tests/test_data.py
@@ -2760,6 +2760,24 @@ def test_power_transformer_constant_feature(standardize):
             assert_allclose(Xt_, X)
 
 
+def test_yeo_johnson_inverse_transform_warning():
+    """Check if a warning is triggered when the inverse transformations of the
+    Box-Cox and Yeo-Johnson transformers return NaN values."""
+    trans = PowerTransformer(method="yeo-johnson")
+    x = np.array([1, 1, 1e10]).reshape(-1, 1)  # extreme skew
+    trans.fit(x)
+    lmbda = trans.lambdas_[0]
+    assert lmbda < 0  # Should be negative
+
+    # any value `psi` for which lambda * psi + 1 <= 0 will result in nan due
+    # to lacking support
+    psi = np.array([10]).reshape(-1, 1)
+    with pytest.warns(UserWarning, match="Some values in column"):
+        x_inv = trans.inverse_transform(psi).item()
+
+    assert np.isnan(x_inv)
+
+
 @pytest.mark.skipif(
     sp_version < parse_version("1.12"),
     reason="scipy version 1.12 required for stable yeo-johnson",