diff --git a/doc/source/whatsnew/v0.19.0.txt b/doc/source/whatsnew/v0.19.0.txt
index 4cc16aac15f8b..7d3889505e098 100644
--- a/doc/source/whatsnew/v0.19.0.txt
+++ b/doc/source/whatsnew/v0.19.0.txt
@@ -229,6 +229,13 @@ Other enhancements
 - ``pd.read_html()`` has gained support for the ``decimal`` option (:issue:`12907`)
 - A top-level function :func:`union_categorical` has been added for combining categoricals, see :ref:`Unioning Categoricals<categorical.union>` (:issue:`13361`)
 - ``Series`` has gained the properties ``.is_monotonic``, ``.is_monotonic_increasing``, ``.is_monotonic_decreasing``, similar to ``Index`` (:issue:`13336`)
+- ``DataFrame`` has gained support to re-order the columns based on the values in a row using ``df.sort_values(by='index_label', axis=1)`` (:issue:`10806`)
+
+  .. ipython:: python
+
+     df = pd.DataFrame({'A': [2, 7], 'B': [3, 5], 'C': [4, 8]},
+                       index=['row1', 'row2'])
+     df.sort_values(by='row2', axis=1)
 
 .. _whatsnew_0190.api:
 
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index b4509c999a5da..92440731c77e2 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -3127,9 +3127,8 @@ def sort_values(self, by, axis=0, ascending=True, inplace=False,
                     kind='quicksort', na_position='last'):
 
         axis = self._get_axis_number(axis)
+        other_axis = 0 if axis == 1 else 1
 
-        if axis != 0:
-            raise ValueError('When sorting by column, axis must be 0 (rows)')
         if not isinstance(by, list):
             by = [by]
         if com.is_sequence(ascending) and len(by) != len(ascending):
@@ -3145,7 +3144,7 @@ def trans(v):
 
             keys = []
             for x in by:
-                k = self[x].values
+                k = self.xs(x, axis=other_axis).values
                 if k.ndim == 2:
                     raise ValueError('Cannot sort by duplicate column %s' %
                                      str(x))
@@ -3157,7 +3156,7 @@ def trans(v):
             from pandas.core.groupby import _nargsort
 
             by = by[0]
-            k = self[by].values
+            k = self.xs(by, axis=other_axis).values
             if k.ndim == 2:
 
                 # try to be helpful
diff --git a/pandas/tests/frame/test_sorting.py b/pandas/tests/frame/test_sorting.py
index 4d57216c8f870..b7a38e9e13ebd 100644
--- a/pandas/tests/frame/test_sorting.py
+++ b/pandas/tests/frame/test_sorting.py
@@ -84,7 +84,7 @@ def test_sort_values(self):
         frame = DataFrame([[1, 1, 2], [3, 1, 0], [4, 5, 6]],
                           index=[1, 2, 3], columns=list('ABC'))
 
-        # by column
+        # by column (axis=0)
         sorted_df = frame.sort_values(by='A')
         indexer = frame['A'].argsort().values
         expected = frame.ix[frame.index[indexer]]
@@ -116,9 +116,26 @@ def test_sort_values(self):
         self.assertRaises(ValueError, lambda: frame.sort_values(
             by=['A', 'B'], axis=2, inplace=True))
 
-        msg = 'When sorting by column, axis must be 0'
-        with assertRaisesRegexp(ValueError, msg):
-            frame.sort_values(by='A', axis=1)
+        # by row (axis=1): GH 10806
+        sorted_df = frame.sort_values(by=3, axis=1)
+        expected = frame
+        assert_frame_equal(sorted_df, expected)
+
+        sorted_df = frame.sort_values(by=3, axis=1, ascending=False)
+        expected = frame.reindex(columns=['C', 'B', 'A'])
+        assert_frame_equal(sorted_df, expected)
+
+        sorted_df = frame.sort_values(by=[1, 2], axis='columns')
+        expected = frame.reindex(columns=['B', 'A', 'C'])
+        assert_frame_equal(sorted_df, expected)
+
+        sorted_df = frame.sort_values(by=[1, 3], axis=1,
+                                      ascending=[True, False])
+        assert_frame_equal(sorted_df, expected)
+
+        sorted_df = frame.sort_values(by=[1, 3], axis=1, ascending=False)
+        expected = frame.reindex(columns=['C', 'B', 'A'])
+        assert_frame_equal(sorted_df, expected)
 
         msg = r'Length of ascending \(5\) != length of by \(2\)'
         with assertRaisesRegexp(ValueError, msg):
@@ -133,6 +150,11 @@ def test_sort_values_inplace(self):
         expected = frame.sort_values(by='A')
         assert_frame_equal(sorted_df, expected)
 
+        sorted_df = frame.copy()
+        sorted_df.sort_values(by=1, axis=1, inplace=True)
+        expected = frame.sort_values(by=1, axis=1)
+        assert_frame_equal(sorted_df, expected)
+
         sorted_df = frame.copy()
         sorted_df.sort_values(by='A', ascending=False, inplace=True)
         expected = frame.sort_values(by='A', ascending=False)
@@ -179,6 +201,10 @@ def test_sort_nan(self):
         sorted_df = df.sort_values(['A'], na_position='first', ascending=False)
         assert_frame_equal(sorted_df, expected)
 
+        expected = df.reindex(columns=['B', 'A'])
+        sorted_df = df.sort_values(by=1, axis=1, na_position='first')
+        assert_frame_equal(sorted_df, expected)
+
         # na_position='last', order
         expected = DataFrame(
             {'A': [1, 1, 2, 4, 6, 8, nan],