diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index 49cb78340d104..19ebe46fca302 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -508,7 +508,11 @@ def get_loc(self, key, method=None, tolerance=None):
             # _get_string_slice will handle cases where grp < freqn
             assert grp >= freqn
 
-            if grp == freqn:
+            # BusinessDay is a bit strange. It has a *lower* code, but we never parse
+            # a string as "BusinessDay" resolution, just Day.
+            if grp == freqn or (
+                reso == Resolution.RESO_DAY and self.dtype.freq.name == "B"
+            ):
                 key = Period(asdt, freq=self.freq)
                 loc = self.get_loc(key, method=method, tolerance=tolerance)
                 return loc
diff --git a/pandas/tests/indexes/period/test_indexing.py b/pandas/tests/indexes/period/test_indexing.py
index eaba0bb3793b2..12454c20d2bb4 100644
--- a/pandas/tests/indexes/period/test_indexing.py
+++ b/pandas/tests/indexes/period/test_indexing.py
@@ -693,6 +693,12 @@ def test_get_value(self):
             result2 = idx2.get_value(input2, p1)
         tm.assert_series_equal(result2, expected2)
 
+    def test_loc_str(self):
+        # https://github.com/pandas-dev/pandas/issues/33964
+        index = pd.period_range(start="2000", periods=20, freq="B")
+        series = pd.Series(range(20), index=index)
+        assert series.loc["2000-01-14"] == 9
+
     @pytest.mark.parametrize("freq", ["H", "D"])
     def test_get_value_datetime_hourly(self, freq):
         # get_loc and get_value should treat datetime objects symmetrically