diff --git a/sklearn/cluster/tests/test_spectral.py b/sklearn/cluster/tests/test_spectral.py
index dc79f427afcdf..f5591c7348ebe 100644
--- a/sklearn/cluster/tests/test_spectral.py
+++ b/sklearn/cluster/tests/test_spectral.py
@@ -191,6 +191,10 @@ def test_discretize(n_samples):
         assert adjusted_rand_score(y_true, y_pred) > 0.8
 
 
+# TODO: Remove when pyamg does replaces sp.rand call with np.random.rand
+# https://github.com/scikit-learn/scikit-learn/issues/15913
+@pytest.mark.filterwarnings(
+    "ignore:scipy.rand is deprecated:DeprecationWarning:pyamg.*")
 def test_spectral_clustering_with_arpack_amg_solvers():
     # Test that spectral_clustering is the same for arpack and amg solver
     # Based on toy example from plot_segmentation_toy.py
diff --git a/sklearn/manifold/tests/test_spectral_embedding.py b/sklearn/manifold/tests/test_spectral_embedding.py
index 295367a422f04..f99eae3783c05 100644
--- a/sklearn/manifold/tests/test_spectral_embedding.py
+++ b/sklearn/manifold/tests/test_spectral_embedding.py
@@ -181,6 +181,10 @@ def test_spectral_embedding_callable_affinity(X, seed=36):
     assert _check_with_col_sign_flipping(embed_rbf, embed_callable, 0.05)
 
 
+# TODO: Remove when pyamg does replaces sp.rand call with np.random.rand
+# https://github.com/scikit-learn/scikit-learn/issues/15913
+@pytest.mark.filterwarnings(
+    "ignore:scipy.rand is deprecated:DeprecationWarning:pyamg.*")
 def test_spectral_embedding_amg_solver(seed=36):
     # Test spectral embedding with amg solver
     pytest.importorskip('pyamg')
@@ -211,6 +215,10 @@ def test_spectral_embedding_amg_solver(seed=36):
     assert _check_with_col_sign_flipping(embed_amg, embed_arpack, 1e-5)
 
 
+# TODO: Remove when pyamg does replaces sp.rand call with np.random.rand
+# https://github.com/scikit-learn/scikit-learn/issues/15913
+@pytest.mark.filterwarnings(
+    "ignore:scipy.rand is deprecated:DeprecationWarning:pyamg.*")
 def test_spectral_embedding_amg_solver_failure(seed=36):
     # Test spectral embedding with amg solver failure, see issue #13393
     pytest.importorskip('pyamg')