diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 044361de218df..0ce7fbfe59c9f 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -825,6 +825,7 @@ Sparse
 - Bug in :meth:`SparseArray.max` and :meth:`SparseArray.min` raising ``ValueError`` for arrays with 0 non-null elements (:issue:`43527`)
 - Bug in :meth:`DataFrame.sparse.to_coo` silently converting non-zero fill values to zero (:issue:`24817`)
 - Bug in :class:`SparseArray` comparison methods with an array-like operand of mismatched length raising ``AssertionError`` or unclear ``ValueError`` depending on the input (:issue:`43863`)
+- Bug in :class:`SparseArray` arithmetic methods ``floordiv`` and ``mod`` behaviors when dividing by zero not matching the non-sparse :class:`Series` behavior (:issue:`38172`)
 -
 
 ExtensionArray
diff --git a/pandas/_libs/sparse_op_helper.pxi.in b/pandas/_libs/sparse_op_helper.pxi.in
index c6e65f8b96187..e6a2c7b1b050a 100644
--- a/pandas/_libs/sparse_op_helper.pxi.in
+++ b/pandas/_libs/sparse_op_helper.pxi.in
@@ -42,6 +42,11 @@ cdef inline sparse_t __mod__(sparse_t a, sparse_t b):
 cdef inline sparse_t __floordiv__(sparse_t a, sparse_t b):
     if b == 0:
         if sparse_t is float64_t:
+            # Match non-sparse Series behavior implemented in mask_zero_div_zero
+            if a > 0:
+                return INF
+            elif a < 0:
+                return -INF
             return NaN
         else:
             return 0
diff --git a/pandas/core/arrays/sparse/array.py b/pandas/core/arrays/sparse/array.py
index f69b9868b10e4..17c5320b1e941 100644
--- a/pandas/core/arrays/sparse/array.py
+++ b/pandas/core/arrays/sparse/array.py
@@ -220,6 +220,16 @@ def _sparse_array_op(
             left_sp_values = left.sp_values
             right_sp_values = right.sp_values
 
+        if (
+            name in ["floordiv", "mod"]
+            and (right == 0).any()
+            and left.dtype.kind in ["i", "u"]
+        ):
+            # Match the non-Sparse Series behavior
+            opname = f"sparse_{name}_float64"
+            left_sp_values = left_sp_values.astype("float64")
+            right_sp_values = right_sp_values.astype("float64")
+
         sparse_op = getattr(splib, opname)
 
         with np.errstate(all="ignore"):
diff --git a/pandas/tests/arrays/sparse/test_arithmetics.py b/pandas/tests/arrays/sparse/test_arithmetics.py
index d7c39c0e0708e..012fe61fdba05 100644
--- a/pandas/tests/arrays/sparse/test_arithmetics.py
+++ b/pandas/tests/arrays/sparse/test_arithmetics.py
@@ -34,26 +34,23 @@ class TestSparseArrayArithmetics:
     def _assert(self, a, b):
         tm.assert_numpy_array_equal(a, b)
 
-    def _check_numeric_ops(self, a, b, a_dense, b_dense, mix, op):
+    def _check_numeric_ops(self, a, b, a_dense, b_dense, mix: bool, op):
+        # Check that arithmetic behavior matches non-Sparse Series arithmetic
+
+        if isinstance(a_dense, np.ndarray):
+            expected = op(pd.Series(a_dense), b_dense).values
+        elif isinstance(b_dense, np.ndarray):
+            expected = op(a_dense, pd.Series(b_dense)).values
+        else:
+            raise NotImplementedError
+
         with np.errstate(invalid="ignore", divide="ignore"):
             if mix:
                 result = op(a, b_dense).to_dense()
             else:
                 result = op(a, b).to_dense()
 
-            if op in [operator.truediv, ops.rtruediv]:
-                # pandas uses future division
-                expected = op(a_dense * 1.0, b_dense)
-            else:
-                expected = op(a_dense, b_dense)
-
-            if op in [operator.floordiv, ops.rfloordiv]:
-                # Series sets 1//0 to np.inf, which SparseArray does not do (yet)
-                mask = np.isinf(expected)
-                if mask.any():
-                    expected[mask] = np.nan
-
-            self._assert(result, expected)
+        self._assert(result, expected)
 
     def _check_bool_result(self, res):
         assert isinstance(res, self._klass)
@@ -125,7 +122,7 @@ def test_float_scalar(
     ):
         op = all_arithmetic_functions
 
-        if not np_version_under1p20:
+        if np_version_under1p20:
             if op in [operator.floordiv, ops.rfloordiv]:
                 if op is operator.floordiv and scalar != 0:
                     pass
@@ -158,9 +155,7 @@ def test_float_scalar_comparison(self, kind):
         self._check_comparison_ops(a, 0, values, 0)
         self._check_comparison_ops(a, 3, values, 3)
 
-    def test_float_same_index_without_nans(
-        self, kind, mix, all_arithmetic_functions, request
-    ):
+    def test_float_same_index_without_nans(self, kind, mix, all_arithmetic_functions):
         # when sp_index are the same
         op = all_arithmetic_functions
 
@@ -178,13 +173,12 @@ def test_float_same_index_with_nans(
         op = all_arithmetic_functions
 
         if (
-            not np_version_under1p20
+            np_version_under1p20
             and op is ops.rfloordiv
             and not (mix and kind == "block")
         ):
             mark = pytest.mark.xfail(raises=AssertionError, reason="GH#38172")
             request.node.add_marker(mark)
-
         values = self._base([np.nan, 1, 2, 0, np.nan, 0, 1, 2, 1, np.nan])
         rvalues = self._base([np.nan, 2, 3, 4, np.nan, 0, 1, 3, 2, np.nan])
 
@@ -360,11 +354,7 @@ def test_bool_array_logical(self, kind, fill_value):
     def test_mixed_array_float_int(self, kind, mix, all_arithmetic_functions, request):
         op = all_arithmetic_functions
 
-        if (
-            not np_version_under1p20
-            and op in [operator.floordiv, ops.rfloordiv]
-            and mix
-        ):
+        if np_version_under1p20 and op in [operator.floordiv, ops.rfloordiv] and mix:
             mark = pytest.mark.xfail(raises=AssertionError, reason="GH#38172")
             request.node.add_marker(mark)