diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index b015495b095b6..4439529faf208 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -310,6 +310,7 @@ Other API Changes
 - Invalid construction of ``IntervalDtype`` will now always raise a ``TypeError`` rather than a ``ValueError`` if the subdtype is invalid (:issue:`21185`)
 - Trying to reindex a ``DataFrame`` with a non unique ``MultiIndex`` now raises a ``ValueError`` instead of an ``Exception`` (:issue:`21770`)
 - :meth:`PeriodIndex.tz_convert` and :meth:`PeriodIndex.tz_localize` have been removed (:issue:`21781`)
+- :class:`Index` subtraction will attempt to operate element-wise instead of raising ``TypeError`` (:issue:`19369`)
 
 .. _whatsnew_0240.deprecations:
 
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 83b70baf4065b..3a42c7963f21b 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -2630,8 +2630,10 @@ def __iadd__(self, other):
         return self + other
 
     def __sub__(self, other):
-        raise TypeError("cannot perform __sub__ with this index type: "
-                        "{typ}".format(typ=type(self).__name__))
+        return Index(np.array(self) - other)
+
+    def __rsub__(self, other):
+        return Index(other - np.array(self))
 
     def __and__(self, other):
         return self.intersection(other)
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index 7b105390db40b..754703dfc4bee 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -3,7 +3,7 @@
 import pytest
 
 from datetime import datetime, timedelta
-
+from decimal import Decimal
 from collections import defaultdict
 
 import pandas.util.testing as tm
@@ -864,13 +864,47 @@ def test_add(self):
         expected = Index(['1a', '1b', '1c'])
         tm.assert_index_equal('1' + index, expected)
 
-    def test_sub(self):
+    def test_sub_fail(self):
         index = self.strIndex
         pytest.raises(TypeError, lambda: index - 'a')
         pytest.raises(TypeError, lambda: index - index)
         pytest.raises(TypeError, lambda: index - index.tolist())
         pytest.raises(TypeError, lambda: index.tolist() - index)
 
+    def test_sub_object(self):
+        # GH#19369
+        index = pd.Index([Decimal(1), Decimal(2)])
+        expected = pd.Index([Decimal(0), Decimal(1)])
+
+        result = index - Decimal(1)
+        tm.assert_index_equal(result, expected)
+
+        result = index - pd.Index([Decimal(1), Decimal(1)])
+        tm.assert_index_equal(result, expected)
+
+        with pytest.raises(TypeError):
+            index - 'foo'
+
+        with pytest.raises(TypeError):
+            index - np.array([2, 'foo'])
+
+    def test_rsub_object(self):
+        # GH#19369
+        index = pd.Index([Decimal(1), Decimal(2)])
+        expected = pd.Index([Decimal(1), Decimal(0)])
+
+        result = Decimal(2) - index
+        tm.assert_index_equal(result, expected)
+
+        result = np.array([Decimal(2), Decimal(2)]) - index
+        tm.assert_index_equal(result, expected)
+
+        with pytest.raises(TypeError):
+            'foo' - index
+
+        with pytest.raises(TypeError):
+            np.array([True, pd.Timestamp.now()]) - index
+
     def test_map_identity_mapping(self):
         # GH 12766
         # TODO: replace with fixture