diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index 13b60f7f05352..c35a0abb3a389 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -881,6 +881,7 @@ Indexing
 - Bug in :func:`~DataFrame.describe` when formatting percentiles in the resulting index showed more decimals than needed (:issue:`46362`)
 - Bug in :meth:`DataFrame.compare` does not recognize differences when comparing ``NA`` with value in nullable dtypes (:issue:`48939`)
 - Bug in :meth:`DataFrame.isetitem` coercing extension array dtypes in :class:`DataFrame` to object (:issue:`49922`)
+- Bug in :class:`BusinessHour` would cause creation of :class:`DatetimeIndex` to fail when no opening hour was included in the index (:issue:`49835`)
 -
 
 Missing
diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index 0bc9751694e9f..b59d17321d8bf 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -1847,15 +1847,20 @@ cdef class BusinessHour(BusinessMixin):
         earliest_start = self.start[0]
         latest_start = self.start[-1]
 
+        if self.n == 0:
+            is_same_sign = sign > 0
+        else:
+            is_same_sign = self.n * sign >= 0
+
         if not self.next_bday.is_on_offset(other):
             # today is not business day
             other = other + sign * self.next_bday
-            if self.n * sign >= 0:
+            if is_same_sign:
                 hour, minute = earliest_start.hour, earliest_start.minute
             else:
                 hour, minute = latest_start.hour, latest_start.minute
         else:
-            if self.n * sign >= 0:
+            if is_same_sign:
                 if latest_start < other.time():
                     # current time is after latest starting time in today
                     other = other + sign * self.next_bday
diff --git a/pandas/tests/tseries/offsets/test_business_hour.py b/pandas/tests/tseries/offsets/test_business_hour.py
index 79e7a5ff67010..319cc053d5d7d 100644
--- a/pandas/tests/tseries/offsets/test_business_hour.py
+++ b/pandas/tests/tseries/offsets/test_business_hour.py
@@ -241,6 +241,12 @@ def test_sub(self, dt, offset2, _offset):
 
         assert dt - offset2 == dt + _offset(-3)
 
+    def test_multiply_by_zero(self, dt, offset1, offset2):
+        assert dt - 0 * offset1 == dt
+        assert dt + 0 * offset1 == dt
+        assert dt - 0 * offset2 == dt
+        assert dt + 0 * offset2 == dt
+
     def testRollback1(
         self,
         dt,
@@ -972,6 +978,12 @@ def test_datetimeindex(self):
         for idx in [idx1, idx2, idx3]:
             tm.assert_index_equal(idx, expected)
 
+    def test_short_datetimeindex_creation(self):
+        # gh-49835
+        idx4 = date_range(start="2014-07-01 10:00", freq="BH", periods=1)
+        expected4 = DatetimeIndex(["2014-07-01 10:00"], freq="BH")
+        tm.assert_index_equal(idx4, expected4)
+
     def test_bday_ignores_timedeltas(self):
         idx = date_range("2010/02/01", "2010/02/10", freq="12H")
         t1 = idx + BDay(offset=Timedelta(3, unit="H"))