diff --git a/doc/source/whatsnew/v0.22.0.txt b/doc/source/whatsnew/v0.22.0.txt
index 37032ff6bc313..9dc10a09378f8 100644
--- a/doc/source/whatsnew/v0.22.0.txt
+++ b/doc/source/whatsnew/v0.22.0.txt
@@ -138,6 +138,7 @@ Other Enhancements
 - :func:`Series` / :func:`DataFrame` tab completion also returns identifiers in the first level of a :func:`MultiIndex`. (:issue:`16326`)
 - :func:`read_excel()` has gained the ``nrows`` parameter (:issue:`16645`)
 - :func:``DataFrame.to_json`` and ``Series.to_json`` now accept an ``index`` argument which allows the user to exclude the index from the JSON output (:issue:`17394`)
+- ``IntervalIndex.to_tuples()`` has gained the ``na_tuple`` parameter to control whether NA is returned as a tuple of NA, or NA itself (:issue:`18756`)
 
 .. _whatsnew_0220.api_breaking:
 
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index 292b0f638f821..cb786574909db 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -544,9 +544,31 @@ def from_tuples(cls, data, closed='right', name=None, copy=False):
 
         return cls.from_arrays(left, right, closed, name=name, copy=False)
 
-    def to_tuples(self):
-        """Return an Index of tuples of the form (left, right)"""
-        return Index(_asarray_tuplesafe(zip(self.left, self.right)))
+    def to_tuples(self, na_tuple=True):
+        """
+        Return an Index of tuples of the form (left, right)
+
+        Parameters
+        ----------
+        na_tuple : boolean, default True
+            Returns NA as a tuple if True, ``(nan, nan)``, or just as the NA
+            value itself if False, ``nan``.
+
+            ..versionadded:: 0.22.0
+
+        Examples
+        --------
+        >>>  idx = pd.IntervalIndex.from_arrays([0, np.nan, 2], [1, np.nan, 3])
+        >>>  idx.to_tuples()
+        Index([(0.0, 1.0), (nan, nan), (2.0, 3.0)], dtype='object')
+        >>>  idx.to_tuples(na_tuple=False)
+        Index([(0.0, 1.0), nan, (2.0, 3.0)], dtype='object')
+        """
+        tuples = _asarray_tuplesafe(zip(self.left, self.right))
+        if not na_tuple:
+            # GH 18756
+            tuples = np.where(~self._isnan, tuples, np.nan)
+        return Index(tuples)
 
     @cache_readonly
     def _multiindex(self):
diff --git a/pandas/tests/indexes/test_interval.py b/pandas/tests/indexes/test_interval.py
index abad930793d7f..c809127a66ab8 100644
--- a/pandas/tests/indexes/test_interval.py
+++ b/pandas/tests/indexes/test_interval.py
@@ -7,6 +7,7 @@
     Interval, IntervalIndex, Index, isna, notna, interval_range, Timestamp,
     Timedelta, compat, date_range, timedelta_range, DateOffset)
 from pandas.compat import lzip
+from pandas.core.common import _asarray_tuplesafe
 from pandas.tseries.offsets import Day
 from pandas._libs.interval import IntervalTree
 from pandas.tests.indexes.common import Base
@@ -1072,6 +1073,45 @@ def test_is_non_overlapping_monotonic(self, closed):
             idx = IntervalIndex.from_breaks(range(4), closed=closed)
             assert idx.is_non_overlapping_monotonic is True
 
+    @pytest.mark.parametrize('tuples', [
+        lzip(range(10), range(1, 11)),
+        lzip(date_range('20170101', periods=10),
+             date_range('20170101', periods=10)),
+        lzip(timedelta_range('0 days', periods=10),
+             timedelta_range('1 day', periods=10))])
+    def test_to_tuples(self, tuples):
+        # GH 18756
+        idx = IntervalIndex.from_tuples(tuples)
+        result = idx.to_tuples()
+        expected = Index(_asarray_tuplesafe(tuples))
+        tm.assert_index_equal(result, expected)
+
+    @pytest.mark.parametrize('tuples', [
+        lzip(range(10), range(1, 11)) + [np.nan],
+        lzip(date_range('20170101', periods=10),
+             date_range('20170101', periods=10)) + [np.nan],
+        lzip(timedelta_range('0 days', periods=10),
+             timedelta_range('1 day', periods=10)) + [np.nan]])
+    @pytest.mark.parametrize('na_tuple', [True, False])
+    def test_to_tuples_na(self, tuples, na_tuple):
+        # GH 18756
+        idx = IntervalIndex.from_tuples(tuples)
+        result = idx.to_tuples(na_tuple=na_tuple)
+
+        # check the non-NA portion
+        expected_notna = Index(_asarray_tuplesafe(tuples[:-1]))
+        result_notna = result[:-1]
+        tm.assert_index_equal(result_notna, expected_notna)
+
+        # check the NA portion
+        result_na = result[-1]
+        if na_tuple:
+            assert isinstance(result_na, tuple)
+            assert len(result_na) == 2
+            assert all(isna(x) for x in result_na)
+        else:
+            assert isna(result_na)
+
 
 class TestIntervalRange(object):