diff --git a/doc/source/whatsnew/v0.20.2.txt b/doc/source/whatsnew/v0.20.2.txt
index 1f71710d19e44..ecbfee862353a 100644
--- a/doc/source/whatsnew/v0.20.2.txt
+++ b/doc/source/whatsnew/v0.20.2.txt
@@ -89,6 +89,7 @@ Reshaping
 - Bug in ``pd.wide_to_long()`` where no error was raised when ``i`` was not a unique identifier (:issue:`16382`)
 - Bug in ``Series.isin(..)`` with a list of tuples (:issue:`16394`)
 - Bug in construction of a ``DataFrame`` with mixed dtypes including an all-NaT column. (:issue:`16395`)
+- Bug in ``DataFrame.agg()`` and ``Series.agg()`` with aggregating on non-callable attributes (:issue:`16405`)
 
 
 Numeric
diff --git a/pandas/core/base.py b/pandas/core/base.py
index a3ef24c80f883..97c4c8626dcbb 100644
--- a/pandas/core/base.py
+++ b/pandas/core/base.py
@@ -378,7 +378,7 @@ def aggregate(self, func, *args, **kwargs):
     def _try_aggregate_string_function(self, arg, *args, **kwargs):
         """
         if arg is a string, then try to operate on it:
-        - try to find a function on ourselves
+        - try to find a function (or attribute) on ourselves
         - try to find a numpy function
         - raise
 
@@ -387,7 +387,15 @@ def _try_aggregate_string_function(self, arg, *args, **kwargs):
 
         f = getattr(self, arg, None)
         if f is not None:
-            return f(*args, **kwargs)
+            if callable(f):
+                return f(*args, **kwargs)
+
+            # people may try to aggregate on a non-callable attribute
+            # but don't let them think they can pass args to it
+            assert len(args) == 0
+            assert len([kwarg for kwarg in kwargs
+                        if kwarg not in ['axis', '_level']]) == 0
+            return f
 
         f = getattr(np, arg, None)
         if f is not None:
diff --git a/pandas/tests/frame/test_apply.py b/pandas/tests/frame/test_apply.py
index aa7c7a7120c1b..a6f39cabb60ed 100644
--- a/pandas/tests/frame/test_apply.py
+++ b/pandas/tests/frame/test_apply.py
@@ -635,3 +635,48 @@ def test_nuiscance_columns(self):
         expected = DataFrame([[6, 6., 'foobarbaz']],
                              index=['sum'], columns=['A', 'B', 'C'])
         assert_frame_equal(result, expected)
+
+    def test_non_callable_aggregates(self):
+
+        # GH 16405
+        # 'size' is a property of frame/series
+        # validate that this is working
+        df = DataFrame({'A': [None, 2, 3],
+                        'B': [1.0, np.nan, 3.0],
+                        'C': ['foo', None, 'bar']})
+
+        # Function aggregate
+        result = df.agg({'A': 'count'})
+        expected = pd.Series({'A': 2})
+
+        assert_series_equal(result, expected)
+
+        # Non-function aggregate
+        result = df.agg({'A': 'size'})
+        expected = pd.Series({'A': 3})
+
+        assert_series_equal(result, expected)
+
+        # Mix function and non-function aggs
+        result1 = df.agg(['count', 'size'])
+        result2 = df.agg({'A': ['count', 'size'],
+                          'B': ['count', 'size'],
+                          'C': ['count', 'size']})
+        expected = pd.DataFrame({'A': {'count': 2, 'size': 3},
+                                 'B': {'count': 2, 'size': 3},
+                                 'C': {'count': 2, 'size': 3}})
+
+        assert_frame_equal(result1, result2, check_like=True)
+        assert_frame_equal(result2, expected, check_like=True)
+
+        # Just functional string arg is same as calling df.arg()
+        result = df.agg('count')
+        expected = df.count()
+
+        assert_series_equal(result, expected)
+
+        # Just a string attribute arg same as calling df.arg
+        result = df.agg('size')
+        expected = df.size
+
+        assert result == expected
diff --git a/pandas/tests/series/test_apply.py b/pandas/tests/series/test_apply.py
index c273d3161fff5..2c5f0d7772cc2 100644
--- a/pandas/tests/series/test_apply.py
+++ b/pandas/tests/series/test_apply.py
@@ -306,6 +306,22 @@ def test_reduce(self):
                           name=self.series.name)
         assert_series_equal(result, expected)
 
+    def test_non_callable_aggregates(self):
+        # test agg using non-callable series attributes
+        s = Series([1, 2, None])
+
+        # Calling agg w/ just a string arg same as calling s.arg
+        result = s.agg('size')
+        expected = s.size
+        assert result == expected
+
+        # test when mixed w/ callable reducers
+        result = s.agg(['size', 'count', 'mean'])
+        expected = Series(OrderedDict({'size': 3.0,
+                                       'count': 2.0,
+                                       'mean': 1.5}))
+        assert_series_equal(result[expected.index], expected)
+
 
 class TestSeriesMap(TestData):