diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 8053c17437c5e..319cda773b693 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -5866,7 +5866,9 @@ def shift(
         freq: Frequency | None = None,
         axis: Axis = 0,
         fill_value: Hashable = lib.no_default,
+        prefix: str | None = None,
         suffix: str | None = None,
+        sep: str ="_",
     ) -> DataFrame:
         if freq is not None and fill_value is not lib.no_default:
             # GH#53832
@@ -5899,11 +5901,17 @@ def shift(
                 shifted_dataframes.append(
                     super()
                     .shift(periods=period, freq=freq, axis=axis, fill_value=fill_value)
+                    .add_prefix(f"{prefix}{sep}" if prefix else "")
                     .add_suffix(f"{suffix}_{period}" if suffix else f"_{period}")
+                    .rename(
+                        columns=lambda col: col.replace(f"{sep}{sep}", sep)
+                    )
                 )
             return concat(shifted_dataframes, axis=1)
         elif suffix:
             raise ValueError("Cannot specify `suffix` if `periods` is an int.")
+        elif prefix:
+            raise ValueError("Cannot specify `prefix` if `periods` is an int.")
         periods = cast(int, periods)
 
         ncols = len(self.columns)
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 8aae4609b1833..bf3ff1f954741 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -10112,13 +10112,17 @@ def mask(
         )
 
     @doc(klass=_shared_doc_kwargs["klass"])
+    if self.ndim == 1 and (prefix or suffix):
+        raise ValueError("`prefix` and `suffix` are only supported on DataFrame.shift when `periods` is a list. ")
     def shift(
         self,
         periods: int | Sequence[int] = 1,
         freq=None,
         axis: Axis = 0,
         fill_value: Hashable = lib.no_default,
+        prefix: str | None = None,
         suffix: str | None = None,
+        sep: str = "_"
     ) -> Self | DataFrame:
         """
         Shift index by desired number of periods with an optional time `freq`.
diff --git a/pandas/tests/frame/methods/test_shift.py b/pandas/tests/frame/methods/test_shift.py
index b52240c208493..00de4653813bf 100644
--- a/pandas/tests/frame/methods/test_shift.py
+++ b/pandas/tests/frame/methods/test_shift.py
@@ -725,6 +725,16 @@ def test_shift_with_iterable_check_other_arguments(self):
         expected = DataFrame({"a_suffix_0": [1, 2], "a_suffix_1": [np.nan, 1.0]})
         tm.assert_frame_equal(shifted, expected)
 
+        # test prefix and sep
+        shifted = df[["a"]].shift(shifts, prefix="pre", suffix="suf", sep="-")
+        expected = DataFrame(
+            {
+                "pre-a-suf-0": [1, 2],
+                "pre-a-suf-1": [np.nan, 1.0]
+            }
+        )
+        tm.assert_frame_equal(shifted, expected)
+
         # check bad inputs when doing multiple shifts
         msg = "If `periods` contains multiple shifts, `axis` cannot be 1."
         with pytest.raises(ValueError, match=msg):
diff --git a/pandas/tests/series/methods/test_diff.py b/pandas/tests/series/methods/test_diff.py
index 89c34aeb64206..1b5d9d2de1bb0 100644
--- a/pandas/tests/series/methods/test_diff.py
+++ b/pandas/tests/series/methods/test_diff.py
@@ -1,5 +1,6 @@
 import numpy as np
 import pytest
+import pandas as pd
 
 from pandas import (
     Series,
@@ -89,3 +90,12 @@ def test_diff_object_dtype(self):
         result = ser.diff()
         expected = ser - ser.shift(1)
         tm.assert_series_equal(result, expected)
+
+def test_series_shift_rejects_prefix_suffix():
+    s = pd.Series([1, 2, 3])
+    
+    with pytest.raises(ValueError, match="prefix.*DataFrame.shift"):
+        s.shift(1, prefix="PRE")
+
+    with pytest.raises(ValueError, match="suffix.*DataFrame.shift"):
+        s.shift(1, suffix="POST")