diff --git a/doc/source/whatsnew/v2.0.1.rst b/doc/source/whatsnew/v2.0.1.rst
index 2e8e2345d4c0a..6a333f00a63ba 100644
--- a/doc/source/whatsnew/v2.0.1.rst
+++ b/doc/source/whatsnew/v2.0.1.rst
@@ -38,6 +38,7 @@ Bug fixes
 - Bug in :meth:`Series.dt.tz_localize` incorrectly localizing timestamps with :class:`ArrowDtype` (:issue:`52677`)
 - Bug in logical and comparison operations between :class:`ArrowDtype` and numpy masked types (e.g. ``"boolean"``) (:issue:`52625`)
 - Fixed bug in :func:`merge` when merging with ``ArrowDtype`` one one and a NumPy dtype on the other side (:issue:`52406`)
+- Fixed bug in :meth:`DataFrame.first` when used with a :class:`DateOffset` (:issue:`45908`)
 - Fixed segfault in :meth:`Series.to_numpy` with ``null[pyarrow]`` dtype (:issue:`52443`)
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index bf8cf831b942a..fb2479b2d58a8 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -41,6 +41,7 @@
     Period,
     Tick,
     Timestamp,
+    offsets,
     to_offset,
 )
 from pandas._typing import (
@@ -9091,8 +9092,17 @@ def first(self, offset) -> Self:
         if len(self.index) == 0:
             return self.copy(deep=False)
 
-        offset = to_offset(offset)
-        if not isinstance(offset, Tick) and offset.is_on_offset(self.index[0]):
+        if isinstance(offset, offsets.DateOffset):
+            input_is_offset = True
+        else:
+            input_is_offset = False
+            offset = to_offset(offset)
+
+        if (
+            not isinstance(offset, Tick)
+            and offset.is_on_offset(self.index[0])
+            and not input_is_offset
+        ):
             # GH#29623 if first value is end of period, remove offset with n = 1
             #  before adding the real offset
             end_date = end = self.index[0] - offset.base + offset
@@ -9100,7 +9110,7 @@ def first(self, offset) -> Self:
             end_date = end = self.index[0] + offset
 
         # Tick-like, e.g. 3 weeks
-        if isinstance(offset, Tick) and end_date in self.index:
+        if isinstance(offset, Tick) or input_is_offset and end_date in self.index:
             end = self.index.searchsorted(end_date, side="left")
             return self.iloc[:end]
 
diff --git a/pandas/tests/frame/methods/test_first_and_last.py b/pandas/tests/frame/methods/test_first_and_last.py
index 64f6665ecd709..4e285832b6b8b 100644
--- a/pandas/tests/frame/methods/test_first_and_last.py
+++ b/pandas/tests/frame/methods/test_first_and_last.py
@@ -1,6 +1,7 @@
 """
 Note: includes tests for `last`
 """
+import numpy as np
 import pytest
 
 import pandas as pd
@@ -95,3 +96,50 @@ def test_empty_not_input(self, func):
         result = getattr(df, func)(offset=1)
         tm.assert_frame_equal(df, result)
         assert df is not result
+
+    @pytest.mark.parametrize("start, periods", [("2010-03-31", 1), ("2010-03-30", 2)])
+    def test_last_day_of_months_with_date_offset(self, frame_or_series, start, periods):
+        x = frame_or_series([1] * 100, index=pd.date_range(start, periods=100))
+        result = x.first(pd.DateOffset(days=periods))
+        expected = frame_or_series(
+            [1] * periods, index=pd.date_range(start, periods=periods)
+        )
+        tm.assert_equal(result, expected)
+
+    def test_date_offset_multiple_days(self, frame_or_series):
+        x = frame_or_series([1] * 100, index=pd.date_range("2010-03-31", periods=100))
+        result = x.first(pd.DateOffset(days=2))
+        expected = frame_or_series(
+            [1] * 2, index=pd.date_range("2010-03-31", "2010-04-01")
+        )
+        tm.assert_equal(result, expected)
+
+    def test_first_with_date_offset(self):
+        # GH#51284
+        i = pd.to_datetime(["2018-04-09", "2018-04-10", "2018-04-11", "2018-04-12"])
+        x = DataFrame({"A": [1, 2, 3, 4]}, index=i)
+        result = x.first(pd.DateOffset(days=2))
+        expected = DataFrame(
+            {"A": [1, 2]}, index=pd.to_datetime(["2018-04-09", "2018-04-10"])
+        )
+        tm.assert_equal(result, expected)
+
+    def test_date_offset_15_days(self):
+        # GH#45908
+        i = pd.date_range("2018-04-09", periods=30, freq="2D")
+        x = DataFrame({"A": np.arange(30)}, index=i)
+        result = x.first(pd.DateOffset(days=15))
+        i2 = pd.date_range("2018-04-09", periods=8, freq="2D")
+        expected = DataFrame({"A": np.arange(8)}, index=i2)
+        tm.assert_equal(result, expected)
+
+    def test_first_with_date_offset_months(self, frame_or_series):
+        periods = 40
+        x = frame_or_series(
+            [1] * periods, index=pd.date_range("2010-03-31", periods=periods)
+        )
+        result = x.first(pd.DateOffset(months=1))
+        expected = frame_or_series(
+            [1] * 30, index=pd.date_range("2010-03-31", periods=30)
+        )
+        tm.assert_equal(result, expected)