diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index c65502898195a..d1bf38588710b 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -323,6 +323,7 @@ Numeric
 - Bug in :meth:`DataFrame.rank` with ``np.inf`` and mixture of ``np.nan`` and ``np.inf`` (:issue:`32593`)
 - Bug in :meth:`DataFrame.rank` with ``axis=0`` and columns holding incomparable types raising ``IndexError`` (:issue:`38932`)
 - Bug in :func:`select_dtypes` different behavior between Windows and Linux with ``include="int"`` (:issue:`36569`)
+- Bug in :meth:`DataFrame.apply` and :meth:`DataFrame.agg` when passed argument ``func="size"`` would operate on the entire ``DataFrame`` instead of rows or columns (:issue:`39934`)
 -
 
 Conversion
diff --git a/pandas/core/apply.py b/pandas/core/apply.py
index 46b1e5b20ce3a..c7fa298b06a2f 100644
--- a/pandas/core/apply.py
+++ b/pandas/core/apply.py
@@ -159,6 +159,10 @@ def f(x):
     def index(self) -> Index:
         return self.obj.index
 
+    @property
+    def agg_axis(self) -> Index:
+        return self.obj._get_agg_axis(self.axis)
+
     @abc.abstractmethod
     def apply(self) -> FrameOrSeriesUnion:
         pass
@@ -541,17 +545,26 @@ def maybe_apply_str(self) -> Optional[FrameOrSeriesUnion]:
         f = self.f
         if not isinstance(f, str):
             return None
+
+        obj = self.obj
+
+        # TODO: GH 39993 - Avoid special-casing by replacing with lambda
+        if f == "size" and isinstance(obj, ABCDataFrame):
+            # Special-cased because DataFrame.size returns a single scalar
+            value = obj.shape[self.axis]
+            return obj._constructor_sliced(value, index=self.agg_axis, name="size")
+
         # Support for `frame.transform('method')`
         # Some methods (shift, etc.) require the axis argument, others
         # don't, so inspect and insert if necessary.
-        func = getattr(self.obj, f, None)
+        func = getattr(obj, f, None)
         if callable(func):
             sig = inspect.getfullargspec(func)
             if "axis" in sig.args:
                 self.kwargs["axis"] = self.axis
             elif self.axis != 0:
                 raise ValueError(f"Operation {f} does not support axis=1")
-        return self.obj._try_aggregate_string_function(f, *self.args, **self.kwargs)
+        return obj._try_aggregate_string_function(f, *self.args, **self.kwargs)
 
     def maybe_apply_multiple(self) -> Optional[FrameOrSeriesUnion]:
         """
@@ -613,10 +626,6 @@ def values(self):
     def dtypes(self) -> Series:
         return self.obj.dtypes
 
-    @property
-    def agg_axis(self) -> Index:
-        return self.obj._get_agg_axis(self.axis)
-
     def apply(self) -> FrameOrSeriesUnion:
         """ compute the results """
         # dispatch to agg
diff --git a/pandas/tests/apply/test_frame_apply.py b/pandas/tests/apply/test_frame_apply.py
index 083c34ce4b63f..c5d0b215ff4d8 100644
--- a/pandas/tests/apply/test_frame_apply.py
+++ b/pandas/tests/apply/test_frame_apply.py
@@ -1415,11 +1415,21 @@ def test_non_callable_aggregates(how):
 
     tm.assert_series_equal(result, expected)
 
-    # Just a string attribute arg same as calling df.arg
-    result = getattr(df, how)("size")
-    expected = df.size
 
-    assert result == expected
+@pytest.mark.parametrize("how", ["agg", "apply"])
+def test_size_as_str(how, axis):
+    # GH 39934
+    df = DataFrame(
+        {"A": [None, 2, 3], "B": [1.0, np.nan, 3.0], "C": ["foo", None, "bar"]}
+    )
+    # Just a string attribute arg same as calling df.arg
+    # on the columns
+    result = getattr(df, how)("size", axis=axis)
+    if axis == 0 or axis == "index":
+        expected = Series(df.shape[0], index=df.columns, name="size")
+    else:
+        expected = Series(df.shape[1], index=df.index, name="size")
+    tm.assert_series_equal(result, expected)
 
 
 def test_agg_listlike_result():