diff --git a/pandas/core/internals/managers.py b/pandas/core/internals/managers.py
index 81c5810d29456..ff80cccaa20d3 100644
--- a/pandas/core/internals/managers.py
+++ b/pandas/core/internals/managers.py
@@ -409,8 +409,15 @@ def diff(self: T, n: int, axis: AxisInt) -> T:
         axis = self._normalize_axis(axis)
         return self.apply("diff", n=n, axis=axis)
 
-    def interpolate(self: T, **kwargs) -> T:
-        return self.apply("interpolate", **kwargs)
+    def interpolate(self: T, inplace: bool, **kwargs) -> T:
+        if inplace:
+            # TODO(CoW) can be optimized to only copy those blocks that have refs
+            if using_copy_on_write() and any(
+                not self._has_no_reference_block(i) for i in range(len(self.blocks))
+            ):
+                self = self.copy()
+
+        return self.apply("interpolate", inplace=inplace, **kwargs)
 
     def shift(self: T, periods: int, axis: AxisInt, fill_value) -> T:
         axis = self._normalize_axis(axis)
diff --git a/pandas/tests/copy_view/test_methods.py b/pandas/tests/copy_view/test_methods.py
index fbd4bbfb38c27..26038725c544f 100644
--- a/pandas/tests/copy_view/test_methods.py
+++ b/pandas/tests/copy_view/test_methods.py
@@ -1194,6 +1194,22 @@ def test_asfreq_noop(using_copy_on_write):
     tm.assert_frame_equal(df, df_orig)
 
 
+def test_interpolate_creates_copy(using_copy_on_write):
+    # GH#51126
+    df = DataFrame({"a": [1.5, np.nan, 3]})
+    view = df[:]
+    expected = df.copy()
+
+    df.ffill(inplace=True)
+    df.iloc[0, 0] = 100.5
+
+    if using_copy_on_write:
+        tm.assert_frame_equal(view, expected)
+    else:
+        expected = DataFrame({"a": [100.5, 1.5, 3]})
+        tm.assert_frame_equal(view, expected)
+
+
 def test_isetitem(using_copy_on_write):
     df = DataFrame({"a": [1, 2, 3], "b": [4, 5, 6], "c": [7, 8, 9]})
     df_orig = df.copy()