diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index b16ca0a80c5b4..aaec5da8af66f 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -157,7 +157,7 @@ ExtensionArray
 
 Other
 ^^^^^
--
+- Bug in :meth:`Series.rank` incorrectly treating int64 min value as NaN (:issue:`32859`)
 -
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/_libs/algos.pyx b/pandas/_libs/algos.pyx
index 7e90a8cc681ef..958cbd050ed61 100644
--- a/pandas/_libs/algos.pyx
+++ b/pandas/_libs/algos.pyx
@@ -840,7 +840,7 @@ def rank_1d(
     elif rank_t is float64_t:
         mask = np.isnan(values)
     elif rank_t is int64_t:
-        mask = values == NPY_NAT
+        mask = missing.isnaobj(values)
 
         # create copy in case of NPY_NAT
         # values are mutated inplace
diff --git a/pandas/tests/test_algos.py b/pandas/tests/test_algos.py
index 6c6bdb6b1b2bd..6e656eca5e152 100644
--- a/pandas/tests/test_algos.py
+++ b/pandas/tests/test_algos.py
@@ -1769,6 +1769,19 @@ def test_basic(self):
             s = Series([1, 100], dtype=dtype)
             tm.assert_numpy_array_equal(algos.rank(s), exp)
 
+    @pytest.mark.parametrize("dtype", ["int32", "int64"])
+    def test_negative_min_rank(self, dtype):
+        # GH#32859
+        # Check that nan is respected on float64
+        s = pd.Series(np.array([np.inf, np.nan, -np.inf]))
+        expected = pd.Series(np.array([2.0, np.nan, 1.0]))
+        tm.assert_series_equal(s.rank(na_option="keep"), expected)
+
+        # Rank works if coverted to most negative value
+        s = pd.Series(np.array([np.inf, np.nan, -np.inf]).astype(dtype))
+        expected = pd.Series(np.array([2.0, 2.0, 2.0]))
+        tm.assert_series_equal(s.rank(na_option="keep"), expected)
+
     def test_uint64_overflow(self):
         exp = np.array([1, 2], dtype=np.float64)