diff --git a/doc/source/whatsnew/v0.23.2.txt b/doc/source/whatsnew/v0.23.2.txt
index 48efc02480e673..94669c5b02410b 100644
--- a/doc/source/whatsnew/v0.23.2.txt
+++ b/doc/source/whatsnew/v0.23.2.txt
@@ -52,8 +52,9 @@ Bug Fixes
 
 **Conversion**
 
+- Bug in constructing :class:`Index` with an iterator or generator (:issue:`21470`)
 - Bug in :meth:`Series.nlargest` for signed and unsigned integer dtypes when the minimum value is present (:issue:`21426`)
--
+
 
 **Indexing**
 
diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index d466198b648ef6..e22b0d626a2188 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -3,7 +3,6 @@
 import numpy as np
 from warnings import warn
 import textwrap
-import types
 
 from pandas import compat
 from pandas.compat import u, lzip
@@ -28,7 +27,7 @@
     is_categorical,
     is_categorical_dtype,
     is_list_like, is_sequence,
-    is_scalar,
+    is_scalar, is_iterator,
     is_dict_like)
 
 from pandas.core.algorithms import factorize, take_1d, unique1d, take
@@ -2483,7 +2482,7 @@ def _convert_to_list_like(list_like):
     if isinstance(list_like, list):
         return list_like
     if (is_sequence(list_like) or isinstance(list_like, tuple) or
-            isinstance(list_like, types.GeneratorType)):
+            is_iterator(list_like)):
         return list(list_like)
     elif is_scalar(list_like):
         return [list_like]
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 6a56278b0da497..27cc368a696e36 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -428,12 +428,14 @@ def __new__(cls, data=None, dtype=None, copy=False, name=None,
         elif data is None or is_scalar(data):
             cls._scalar_data_error(data)
         else:
-            if tupleize_cols and is_list_like(data) and data:
+            if tupleize_cols and is_list_like(data):
+                # GH21470: convert iterable to list before determining if empty
                 if is_iterator(data):
                     data = list(data)
-                # we must be all tuples, otherwise don't construct
-                # 10697
-                if all(isinstance(e, tuple) for e in data):
+
+                if data and all(isinstance(e, tuple) for e in data):
+                    # we must be all tuples, otherwise don't construct
+                    # 10697
                     from .multi import MultiIndex
                     return MultiIndex.from_tuples(
                         data, names=name or kwargs.get('names'))
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index b8bd218ec25ab3..1d8a958c3413f3 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -445,21 +445,24 @@ def test_constructor_dtypes_timedelta(self, attr, klass):
         result = klass(list(values), dtype=dtype)
         tm.assert_index_equal(result, index)
 
-    def test_constructor_empty_gen(self):
-        skip_index_keys = ["repeats", "periodIndex", "rangeIndex",
-                           "tuples"]
-        for key, index in self.generate_index_types(skip_index_keys):
-            empty = index.__class__([])
-            assert isinstance(empty, index.__class__)
-            assert not len(empty)
+    @pytest.mark.parametrize("value", [[], iter([]), (x for x in [])])
+    @pytest.mark.parametrize("klass",
+                             [Index, Float64Index, Int64Index, UInt64Index,
+                              CategoricalIndex, DatetimeIndex, TimedeltaIndex])
+    def test_constructor_empty(self, value, klass):
+        empty = klass(value)
+        assert isinstance(empty, klass)
+        assert not len(empty)
 
     @pytest.mark.parametrize("empty,klass", [
         (PeriodIndex([], freq='B'), PeriodIndex),
+        (PeriodIndex(iter([]), freq='B'), PeriodIndex),
+        (PeriodIndex((x for x in []), freq='B'), PeriodIndex),
         (RangeIndex(step=1), pd.RangeIndex),
         (MultiIndex(levels=[[1, 2], ['blue', 'red']],
                     labels=[[], []]), MultiIndex)
     ])
-    def test_constructor_empty(self, empty, klass):
+    def test_constructor_empty_special(self, empty, klass):
         assert isinstance(empty, klass)
         assert not len(empty)