diff --git a/pandas/tests/frame/test_rank.py b/pandas/tests/frame/test_rank.py
index 10c42e0d1a1cf..6bb9dea15d1ce 100644
--- a/pandas/tests/frame/test_rank.py
+++ b/pandas/tests/frame/test_rank.py
@@ -310,6 +310,7 @@ def test_rank_pct_true(self, method, exp):
         tm.assert_frame_equal(result, expected)
 
     @pytest.mark.single
+    @pytest.mark.high_memory
     def test_pct_max_many_rows(self):
         # GH 18271
         df = DataFrame({'A': np.arange(2**24 + 1),
diff --git a/pandas/tests/series/test_rank.py b/pandas/tests/series/test_rank.py
index 510a51e002918..dfcda889269ee 100644
--- a/pandas/tests/series/test_rank.py
+++ b/pandas/tests/series/test_rank.py
@@ -499,6 +499,7 @@ def test_rank_first_pct(dtype, ser, exp):
 
 
 @pytest.mark.single
+@pytest.mark.high_memory
 def test_pct_max_many_rows():
         # GH 18271
         s = Series(np.arange(2**24 + 1))
diff --git a/pandas/tests/test_algos.py b/pandas/tests/test_algos.py
index 888cf78a1c66a..cb7426ce2f7c9 100644
--- a/pandas/tests/test_algos.py
+++ b/pandas/tests/test_algos.py
@@ -1484,6 +1484,7 @@ def test_too_many_ndims(self):
             algos.rank(arr)
 
     @pytest.mark.single
+    @pytest.mark.high_memory
     @pytest.mark.parametrize('values', [
         np.arange(2**24 + 1),
         np.arange(2**25 + 2).reshape(2**24 + 1, 2)],