diff --git a/sklearn/metrics/tests/test_pairwise.py b/sklearn/metrics/tests/test_pairwise.py
index e8b9e24a280c1..e2549cbde0807 100644
--- a/sklearn/metrics/tests/test_pairwise.py
+++ b/sklearn/metrics/tests/test_pairwise.py
@@ -505,6 +505,30 @@ def test_pairwise_distances_argmin_min():
     np.testing.assert_almost_equal(dist_orig_ind, dist_chunked_ind, decimal=7)
     np.testing.assert_almost_equal(dist_orig_val, dist_chunked_val, decimal=7)
 
+    # Changing the axis and permuting datasets must give the same results
+    argmin_0, dist_0 = pairwise_distances_argmin_min(X, Y, axis=0)
+    argmin_1, dist_1 = pairwise_distances_argmin_min(Y, X, axis=1)
+
+    assert_allclose(dist_0, dist_1)
+    assert_array_equal(argmin_0, argmin_1)
+
+    argmin_0, dist_0 = pairwise_distances_argmin_min(X, X, axis=0)
+    argmin_1, dist_1 = pairwise_distances_argmin_min(X, X, axis=1)
+
+    assert_allclose(dist_0, dist_1)
+    assert_array_equal(argmin_0, argmin_1)
+
+    # Changing the axis and permuting datasets must give the same results
+    argmin_0 = pairwise_distances_argmin(X, Y, axis=0)
+    argmin_1 = pairwise_distances_argmin(Y, X, axis=1)
+
+    assert_array_equal(argmin_0, argmin_1)
+
+    argmin_0 = pairwise_distances_argmin(X, X, axis=0)
+    argmin_1 = pairwise_distances_argmin(X, X, axis=1)
+
+    assert_array_equal(argmin_0, argmin_1)
+
 
 def _reduce_func(dist, start):
     return dist[:, :100]