diff --git a/doc/whats_new/v1.6.rst b/doc/whats_new/v1.6.rst
index 84838bed686fb..35f18bb125a43 100644
--- a/doc/whats_new/v1.6.rst
+++ b/doc/whats_new/v1.6.rst
@@ -172,6 +172,12 @@ Changelog
   now accepts string format or callable to generate feature names. :pr:`28934` by
   :user:`Marc Bresson <MarcBresson>`.
 
+:mod:`sklearn.cross_decomposition`
+..................................
+
+- |Fix| :class:`cross_decomposition.PLSRegression` properly raises an error when
+  `n_components` is larger than `n_samples`. :pr:`29710` by `Thomas Fan`_.
+
 :mod:`sklearn.datasets`
 .......................
 
diff --git a/sklearn/cross_decomposition/_pls.py b/sklearn/cross_decomposition/_pls.py
index 16024cf961d27..ac1e8035590d6 100644
--- a/sklearn/cross_decomposition/_pls.py
+++ b/sklearn/cross_decomposition/_pls.py
@@ -291,7 +291,9 @@ def fit(self, X, y=None, Y=None):
         # With PLSRegression n_components is bounded by the rank of (X.T X) see
         # Wegelin page 25. With CCA and PLSCanonical, n_components is bounded
         # by the rank of X and the rank of Y: see Wegelin page 12
-        rank_upper_bound = p if self.deflation_mode == "regression" else min(n, p, q)
+        rank_upper_bound = (
+            min(n, p) if self.deflation_mode == "regression" else min(n, p, q)
+        )
         if n_components > rank_upper_bound:
             raise ValueError(
                 f"`n_components` upper bound is {rank_upper_bound}. "
diff --git a/sklearn/cross_decomposition/tests/test_pls.py b/sklearn/cross_decomposition/tests/test_pls.py
index c8de4ad8a78de..381868b9b60b0 100644
--- a/sklearn/cross_decomposition/tests/test_pls.py
+++ b/sklearn/cross_decomposition/tests/test_pls.py
@@ -480,6 +480,17 @@ def test_n_components_upper_bounds(Estimator):
         est.fit(X, Y)
 
 
+def test_n_components_upper_PLSRegression():
+    """Check the validation of `n_components` upper bounds for PLSRegression."""
+    rng = np.random.RandomState(0)
+    X = rng.randn(20, 64)
+    Y = rng.randn(20, 3)
+    est = PLSRegression(n_components=30)
+    err_msg = "`n_components` upper bound is 20. Got 30 instead. Reduce `n_components`."
+    with pytest.raises(ValueError, match=err_msg):
+        est.fit(X, Y)
+
+
 @pytest.mark.parametrize("n_samples, n_features", [(100, 10), (100, 200)])
 def test_singular_value_helpers(n_samples, n_features, global_random_seed):
     # Make sure SVD and power method give approximately the same results