diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 752d08a526d8c..18b67c435b11b 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -211,6 +211,7 @@ Other enhancements
 - :meth:`Series.map` can now accept kwargs to pass on to func (:issue:`59814`)
 - :meth:`Series.map` now accepts an ``engine`` parameter to allow execution with a third-party execution engine (:issue:`61125`)
 - :meth:`Series.rank` and :meth:`DataFrame.rank` with numpy-nullable dtypes preserve ``NA`` values and return ``UInt64`` dtype where appropriate instead of casting ``NA`` to ``NaN`` with ``float64`` dtype (:issue:`62043`)
+- :meth:`Series.round` and :meth:`DataFrame.round` now operate pointwise on columns of object dtype (:issue:`62174`)
 - :meth:`Series.str.get_dummies` now accepts a  ``dtype`` parameter to specify the dtype of the resulting DataFrame (:issue:`47872`)
 - :meth:`pandas.concat` will raise a ``ValueError`` when ``ignore_index=True`` and ``keys`` is not ``None`` (:issue:`59274`)
 - :py:class:`frozenset` elements in pandas objects are now natively printed (:issue:`60690`)
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index a35ef122ed512..bc526c8d48785 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -99,10 +99,8 @@
     is_dataclass,
     is_dict_like,
     is_float,
-    is_float_dtype,
     is_hashable,
     is_integer,
-    is_integer_dtype,
     is_iterator,
     is_list_like,
     is_scalar,
@@ -11560,24 +11558,10 @@ def round(
         def _dict_round(df: DataFrame, decimals) -> Iterator[Series]:
             for col, vals in df.items():
                 try:
-                    yield _series_round(vals, decimals[col])
+                    yield vals.round(decimals[col])
                 except KeyError:
                     yield vals
 
-        def _series_round(ser: Series, decimals: int) -> Series:
-            if is_integer_dtype(ser.dtype) or is_float_dtype(ser.dtype):
-                return ser.round(decimals)
-            elif isinstance(ser._values, (DatetimeArray, TimedeltaArray, PeriodArray)):
-                # GH#57781
-                # TODO: also the ArrowDtype analogues?
-                warnings.warn(
-                    "obj.round has no effect with datetime, timedelta, "
-                    "or period dtypes. Use obj.dt.round(...) instead.",
-                    UserWarning,
-                    stacklevel=find_stack_level(),
-                )
-            return ser
-
         nv.validate_round(args, kwargs)
 
         if isinstance(decimals, (dict, Series)):
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index a9ad561cbc393..02dd396cf5457 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+import functools
 import inspect
 import re
 from typing import (
@@ -345,7 +346,6 @@ def apply(self, func, **kwargs) -> list[Block]:
         one
         """
         result = func(self.values, **kwargs)
-
         result = maybe_coerce_values(result)
         return self._split_op_result(result)
 
@@ -1503,9 +1503,8 @@ def quantile(
     def round(self, decimals: int) -> Self:
         """
         Rounds the values.
-        If the block is not of an integer or float dtype, nothing happens.
-        This is consistent with DataFrame.round behavior.
-        (Note: Series.round would raise)
+        If the block is of object dtype, it will operate pointwise and possibly raise.
+        Otherwise, if the block is not of an integer or float dtype, nothing happens.
 
         Parameters
         ----------
@@ -1513,6 +1512,16 @@ def round(self, decimals: int) -> Self:
             Number of decimal places to round to.
             Caller is responsible for validating this
         """
+        if self.dtype == _dtype_obj:
+            round_func = functools.partial(round, ndigits=decimals)
+            if self.values.ndim == 1:
+                values = algos.map_array(self.values, round_func)
+            else:
+                values = algos.map_array(self.values.ravel(), round_func).reshape(
+                    self.values.shape
+                )
+            return self.make_block_same_class(values, refs=None)
+
         if not self.is_numeric or self.is_bool:
             if isinstance(self.values, (DatetimeArray, TimedeltaArray, PeriodArray)):
                 # GH#57781
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 1a8645cf1815d..2f0e4b520169e 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -2515,8 +2515,6 @@ def round(self, decimals: int = 0, *args, **kwargs) -> Series:
         dtype: float64
         """
         nv.validate_round(args, kwargs)
-        if self.dtype == "object":
-            raise TypeError("Expected numeric dtype, got object instead.")
         new_mgr = self._mgr.round(decimals=decimals)
         return self._constructor_from_mgr(new_mgr, axes=new_mgr.axes).__finalize__(
             self, method="round"
diff --git a/pandas/tests/frame/methods/test_round.py b/pandas/tests/frame/methods/test_round.py
index 5f2566fefca76..2571bbe112772 100644
--- a/pandas/tests/frame/methods/test_round.py
+++ b/pandas/tests/frame/methods/test_round.py
@@ -227,3 +227,41 @@ def test_round_empty_not_input(self):
         result = df.round()
         tm.assert_frame_equal(df, result)
         assert df is not result
+
+    def test_round_object_columns(self):
+        # GH#62174
+        df = DataFrame(
+            {
+                "a": Series([1.1111, 2.2222, 3.3333], dtype="object"),
+                "b": Series([4.4444, 5.5555, 6.6666]),
+                "c": Series([7.7777, 8.8888, 9.9999], dtype="object"),
+            }
+        )
+        result = df.round(2)
+        expected = DataFrame(
+            {
+                "a": Series([1.11, 2.22, 3.33]),
+                "b": Series([4.44, 5.56, 6.67]),
+                "c": Series([7.78, 8.89, 10.0]),
+            }
+        )
+        tm.assert_frame_equal(result, expected)
+
+    def test_round_object_columns_with_dict(self):
+        # GH#62174
+        df = DataFrame(
+            {
+                "a": Series([1.1111, 2.2222, 3.3333], dtype="object"),
+                "b": Series([4.4444, 5.5555, 6.6666]),
+                "c": Series([7.7777, 8.8888, 9.9999], dtype="object"),
+            }
+        )
+        result = df.round({"a": 1, "b": 2, "c": 3})
+        expected = DataFrame(
+            {
+                "a": Series([1.1, 2.2, 3.3]),
+                "b": Series([4.44, 5.56, 6.67]),
+                "c": Series([7.778, 8.889, 10.0]),
+            }
+        )
+        tm.assert_frame_equal(result, expected)
diff --git a/pandas/tests/series/methods/test_round.py b/pandas/tests/series/methods/test_round.py
index a78f77e990ae1..d857f1023c28b 100644
--- a/pandas/tests/series/methods/test_round.py
+++ b/pandas/tests/series/methods/test_round.py
@@ -73,9 +73,16 @@ def test_round_ea_boolean(self):
         result.iloc[0] = False
         tm.assert_series_equal(ser, expected)
 
-    def test_round_dtype_object(self):
-        # GH#61206
-        ser = Series([0.2], dtype="object")
-        msg = "Expected numeric dtype, got object instead."
+    def test_round_numeric_dtype_object(self):
+        # GH#61206, GH#62174
+        ser = Series([0.232], dtype="object")
+        expected = Series([0.2])
+        result = ser.round(1)
+        tm.assert_series_equal(result, expected)
+
+    def test_round_non_numeric_dtype_object(self):
+        # GH#62174
+        ser = Series(["bar"], dtype="object")
+        msg = "Expected numeric entries for dtype object."
         with pytest.raises(TypeError, match=msg):
             ser.round()