diff --git a/doc/source/whatsnew/v0.25.1.rst b/doc/source/whatsnew/v0.25.1.rst
index 124a2ced534c4..44cc38662d976 100644
--- a/doc/source/whatsnew/v0.25.1.rst
+++ b/doc/source/whatsnew/v0.25.1.rst
@@ -55,7 +55,7 @@ Numeric
 - Bug in :meth:`Series.interpolate` when using a timezone aware :class:`DatetimeIndex` (:issue:`27548`)
 - Bug when printing negative floating point complex numbers would raise an ``IndexError`` (:issue:`27484`)
 - Bug where :class:`DataFrame` arithmetic operators such as :meth:`DataFrame.mul` with a :class:`Series` with axis=1 would raise an ``AttributeError`` on :class:`DataFrame` larger than the minimum threshold to invoke numexpr (:issue:`27636`)
--
+- Bug in :class:`DataFrame` arithmetic where missing values in results were incorrectly masked with ``NaN`` instead of ``Inf`` (:issue:`27464`)
 
 Conversion
 ^^^^^^^^^^
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 0570b9af2d256..1f85b31be69b2 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -111,6 +111,7 @@
     sanitize_index,
     to_arrays,
 )
+from pandas.core.ops.missing import dispatch_fill_zeros
 from pandas.core.series import Series
 
 from pandas.io.formats import console, format as fmt
@@ -5365,7 +5366,9 @@ def _arith_op(left, right):
             # iterate over columns
             return ops.dispatch_to_series(this, other, _arith_op)
         else:
-            result = _arith_op(this.values, other.values)
+            with np.errstate(all="ignore"):
+                result = _arith_op(this.values, other.values)
+            result = dispatch_fill_zeros(func, this.values, other.values, result)
             return self._constructor(
                 result, index=new_index, columns=new_columns, copy=False
             )
diff --git a/pandas/tests/arithmetic/test_numeric.py b/pandas/tests/arithmetic/test_numeric.py
index 2b23790e4ccd3..d686d9f90a5a4 100644
--- a/pandas/tests/arithmetic/test_numeric.py
+++ b/pandas/tests/arithmetic/test_numeric.py
@@ -1227,3 +1227,36 @@ def test_addsub_arithmetic(self, dtype, delta):
         tm.assert_index_equal(index + index, 2 * index)
         tm.assert_index_equal(index - index, 0 * index)
         assert not (index - index).empty
+
+
+def test_fill_value_inf_masking():
+    # GH #27464 make sure we mask 0/1 with Inf and not NaN
+    df = pd.DataFrame({"A": [0, 1, 2], "B": [1.1, None, 1.1]})
+
+    other = pd.DataFrame({"A": [1.1, 1.2, 1.3]}, index=[0, 2, 3])
+
+    result = df.rfloordiv(other, fill_value=1)
+
+    expected = pd.DataFrame(
+        {"A": [np.inf, 1.0, 0.0, 1.0], "B": [0.0, np.nan, 0.0, np.nan]}
+    )
+    tm.assert_frame_equal(result, expected)
+
+
+def test_dataframe_div_silenced():
+    # GH#26793
+    pdf1 = pd.DataFrame(
+        {
+            "A": np.arange(10),
+            "B": [np.nan, 1, 2, 3, 4] * 2,
+            "C": [np.nan] * 10,
+            "D": np.arange(10),
+        },
+        index=list("abcdefghij"),
+        columns=list("ABCD"),
+    )
+    pdf2 = pd.DataFrame(
+        np.random.randn(10, 4), index=list("abcdefghjk"), columns=list("ABCX")
+    )
+    with tm.assert_produces_warning(None):
+        pdf1.div(pdf2, fill_value=0)