diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index 039a86da0541e..8bb924f4003a2 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -282,6 +282,7 @@ Indexing
 Missing
 ^^^^^^^
 - Bug in :meth:`Series.fillna` and :meth:`DataFrame.fillna` with ``downcast`` keyword not being respected in some cases where there are no NA values present (:issue:`45423`)
+- Bug in :meth:`DataFrame.interpolate` with object-dtype column not returning a copy with ``inplace=False`` (:issue:`45791`)
 -
 
 MultiIndex
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index a497475ebd182..fcc7e915e2b57 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -6448,7 +6448,6 @@ def fillna(
                 axis=axis,
                 limit=limit,
                 inplace=inplace,
-                coerce=True,
                 downcast=downcast,
             )
         else:
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index 2c1724adf0300..15aa97b065446 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -1023,7 +1023,6 @@ def interpolate(
         limit_direction: str = "forward",
         limit_area: str | None = None,
         fill_value: Any | None = None,
-        coerce: bool = False,
         downcast: str | None = None,
         **kwargs,
     ) -> list[Block]:
@@ -1034,6 +1033,16 @@ def interpolate(
             # If there are no NAs, then interpolate is a no-op
             return [self] if inplace else [self.copy()]
 
+        try:
+            m = missing.clean_fill_method(method)
+        except ValueError:
+            m = None
+        if m is None and self.dtype.kind != "f":
+            # only deal with floats
+            # bc we already checked that can_hold_na, we dont have int dtype here
+            # test_interp_basic checks that we make a copy here
+            return [self] if inplace else [self.copy()]
+
         if self.is_object and self.ndim == 2 and self.shape[0] != 1 and axis == 0:
             # split improves performance in ndarray.copy()
             return self.split_and_operate(
@@ -1046,21 +1055,10 @@ def interpolate(
                 limit_direction,
                 limit_area,
                 fill_value,
-                coerce,
                 downcast,
                 **kwargs,
             )
 
-        try:
-            m = missing.clean_fill_method(method)
-        except ValueError:
-            m = None
-        if m is None and self.dtype.kind != "f":
-            # only deal with floats
-            # bc we already checked that can_hold_na, we dont have int dtype here
-            # TODO: make a copy if not inplace?
-            return [self]
-
         data = self.values if inplace else self.values.copy()
         data = cast(np.ndarray, data)  # bc overridden by ExtensionBlock
 
diff --git a/pandas/tests/frame/methods/test_interpolate.py b/pandas/tests/frame/methods/test_interpolate.py
index 6566d426d9a6b..98f9d2670074d 100644
--- a/pandas/tests/frame/methods/test_interpolate.py
+++ b/pandas/tests/frame/methods/test_interpolate.py
@@ -49,6 +49,38 @@ def test_interp_basic(self):
         result = df.interpolate()
         tm.assert_frame_equal(result, expected)
 
+        # check we didn't operate inplace GH#45791
+        cvalues = df["C"]._values
+        dvalues = df["D"].values
+        assert not np.shares_memory(cvalues, result["C"]._values)
+        assert not np.shares_memory(dvalues, result["D"]._values)
+
+        res = df.interpolate(inplace=True)
+        assert res is None
+        tm.assert_frame_equal(df, expected)
+
+        # check we DID operate inplace
+        assert np.shares_memory(df["C"]._values, cvalues)
+        assert np.shares_memory(df["D"]._values, dvalues)
+
+    def test_interp_basic_with_non_range_index(self):
+        df = DataFrame(
+            {
+                "A": [1, 2, np.nan, 4],
+                "B": [1, 4, 9, np.nan],
+                "C": [1, 2, 3, 5],
+                "D": list("abcd"),
+            }
+        )
+        expected = DataFrame(
+            {
+                "A": [1.0, 2.0, 3.0, 4.0],
+                "B": [1.0, 4.0, 9.0, 9.0],
+                "C": [1, 2, 3, 5],
+                "D": list("abcd"),
+            }
+        )
+
         result = df.set_index("C").interpolate()
         expected = df.set_index("C")
         expected.loc[3, "A"] = 3