diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 25234489167b2..12f522301e121 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -983,6 +983,7 @@ Datetimelike
 - Bug in :meth:`DataFrame.min` and :meth:`DataFrame.max` casting ``datetime64`` and ``timedelta64`` columns to ``float64`` and losing precision (:issue:`60850`)
 - Bug in :meth:`Dataframe.agg` with df with missing values resulting in IndexError (:issue:`58810`)
 - Bug in :meth:`DateOffset.rollback` (and subclass methods) with ``normalize=True`` rolling back one offset too long (:issue:`32616`)
+- Bug in :meth:`DatetimeIndex.asof` with a string key giving incorrect results (:issue:`50946`)
 - Bug in :meth:`DatetimeIndex.is_year_start` and :meth:`DatetimeIndex.is_quarter_start` does not raise on Custom business days frequencies bigger then "1C" (:issue:`58664`)
 - Bug in :meth:`DatetimeIndex.is_year_start` and :meth:`DatetimeIndex.is_quarter_start` returning ``False`` on double-digit frequencies (:issue:`58523`)
 - Bug in :meth:`DatetimeIndex.union` and :meth:`DatetimeIndex.intersection` when ``unit`` was non-nanosecond (:issue:`59036`)
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 93b615fe7b101..72f7a1e086b60 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -5675,7 +5675,7 @@ def asof(self, label):
                 return self._na_value
         else:
             if isinstance(loc, slice):
-                loc = loc.indices(len(self))[-1]
+                return self[loc][-1]
 
         return self[loc]
 
diff --git a/pandas/tests/indexes/datetimes/methods/test_asof.py b/pandas/tests/indexes/datetimes/methods/test_asof.py
index dc92f533087bc..41415f2a37337 100644
--- a/pandas/tests/indexes/datetimes/methods/test_asof.py
+++ b/pandas/tests/indexes/datetimes/methods/test_asof.py
@@ -1,6 +1,7 @@
 from datetime import timedelta
 
 from pandas import (
+    DatetimeIndex,
     Index,
     Timestamp,
     date_range,
@@ -28,3 +29,18 @@ def test_asof(self):
 
         dt = index[0].to_pydatetime()
         assert isinstance(index.asof(dt), Timestamp)
+
+    def test_asof_datetime_string(self):
+        # GH#50946
+
+        dti = date_range("2021-08-05", "2021-08-10", freq="1D")
+
+        key = "2021-08-09"
+        res = dti.asof(key)
+        exp = dti[4]
+        assert res == exp
+
+        # add a non-midnight time caused a bug
+        dti2 = DatetimeIndex(list(dti) + ["2021-08-11 00:00:01"])
+        res = dti2.asof(key)
+        assert res == exp