diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index ace975385ce32..236b0109da786 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -3642,6 +3642,10 @@ def rename(self, *args, **kwargs):
         level : int or level name, default None
             In case of a MultiIndex, only rename labels in the specified
             level.
+        tupleize_cols : boolean, default False
+            In case of an Index, when True, create MultiIndex if possible.
+            False ensures that an Index will not be converted to a
+            MultiIndex if labels are 'rename'd.
 
         Returns
         -------
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index d5cd22732f0a9..ef0ab2cfce0c4 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -933,6 +933,7 @@ def rename(self, *args, **kwargs):
         inplace = kwargs.pop('inplace', False)
         level = kwargs.pop('level', None)
         axis = kwargs.pop('axis', None)
+        tupleize_cols = kwargs.pop('tupleize_cols', False)
         if axis is not None:
             axis = self._get_axis_number(axis)
 
@@ -970,8 +971,10 @@ def f(x):
             baxis = self._get_block_manager_axis(axis)
             if level is not None:
                 level = self.axes[axis]._get_level_number(level)
-            result._data = result._data.rename_axis(f, axis=baxis, copy=copy,
-                                                    level=level)
+            result._data = \
+                result._data.rename_axis(f, axis=baxis, copy=copy,
+                                         level=level,
+                                         tupleize_cols=tupleize_cols)
             result._clear_item_cache()
 
         if inplace:
diff --git a/pandas/core/internals.py b/pandas/core/internals.py
index a0e122d390240..48ad53ee67f79 100644
--- a/pandas/core/internals.py
+++ b/pandas/core/internals.py
@@ -3280,7 +3280,8 @@ def set_axis(self, axis, new_labels):
 
         self.axes[axis] = new_labels
 
-    def rename_axis(self, mapper, axis, copy=True, level=None):
+    def rename_axis(self, mapper, axis, copy=True, level=None,
+                    tupleize_cols=False):
         """
         Rename one of axes.
 
@@ -3293,7 +3294,8 @@ def rename_axis(self, mapper, axis, copy=True, level=None):
 
         """
         obj = self.copy(deep=copy)
-        obj.set_axis(axis, _transform_index(self.axes[axis], mapper, level))
+        obj.set_axis(axis, _transform_index(self.axes[axis], mapper, level,
+                                            tupleize_cols=tupleize_cols))
         return obj
 
     def add_prefix(self, prefix):
@@ -5234,7 +5236,7 @@ def _safe_reshape(arr, new_shape):
     return arr
 
 
-def _transform_index(index, func, level=None):
+def _transform_index(index, func, level=None, tupleize_cols=True):
     """
     Apply function to all values found in index.
 
@@ -5251,7 +5253,7 @@ def _transform_index(index, func, level=None):
         return MultiIndex.from_tuples(items, names=index.names)
     else:
         items = [func(x) for x in index]
-        return Index(items, name=index.name)
+        return Index(items, name=index.name, tupleize_cols=tupleize_cols)
 
 
 def _putmask_smart(v, m, n):