diff --git a/sklearn/metrics/pairwise.py b/sklearn/metrics/pairwise.py
index f819079aa789e..dd5c4564b0b54 100644
--- a/sklearn/metrics/pairwise.py
+++ b/sklearn/metrics/pairwise.py
@@ -1289,9 +1289,10 @@ def laplacian_kernel(X, Y=None, gamma=None):
     Parameters
     ----------
     X : ndarray of shape (n_samples_X, n_features)
+        A feature array.
 
     Y : ndarray of shape (n_samples_Y, n_features), default=None
-        If `None`, uses `Y=X`.
+        An optional second feature array. If `None`, uses `Y=X`.
 
     gamma : float, default=None
         If None, defaults to 1.0 / n_features.
@@ -1299,6 +1300,7 @@ def laplacian_kernel(X, Y=None, gamma=None):
     Returns
     -------
     kernel_matrix : ndarray of shape (n_samples_X, n_samples_Y)
+        The kernel matrix.
     """
     X, Y = check_pairwise_arrays(X, Y)
     if gamma is None:
diff --git a/sklearn/tests/test_docstrings.py b/sklearn/tests/test_docstrings.py
index e4cb10429c4d2..f469976f80556 100644
--- a/sklearn/tests/test_docstrings.py
+++ b/sklearn/tests/test_docstrings.py
@@ -78,7 +78,6 @@
     "sklearn.metrics.pairwise.distance_metrics",
     "sklearn.metrics.pairwise.haversine_distances",
     "sklearn.metrics.pairwise.kernel_metrics",
-    "sklearn.metrics.pairwise.laplacian_kernel",
     "sklearn.metrics.pairwise.paired_manhattan_distances",
     "sklearn.metrics.pairwise.pairwise_distances_argmin",
     "sklearn.metrics.pairwise.pairwise_distances_argmin_min",