diff --git a/doc/source/whatsnew/v2.3.0.rst b/doc/source/whatsnew/v2.3.0.rst
index fc60789801ce7..f7bd8a8f191ae 100644
--- a/doc/source/whatsnew/v2.3.0.rst
+++ b/doc/source/whatsnew/v2.3.0.rst
@@ -107,6 +107,7 @@ Timezones
 Numeric
 ^^^^^^^
 - Enabled :class:`Series.mode` and :class:`DataFrame.mode` with ``dropna=False`` to sort the result for all dtypes in the presence of NA values; previously only certain dtypes would sort (:issue:`60702`)
+- Bug in :meth:`Series.round` on object columns no longer raises ``TypeError``
 -
 
 Conversion
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 4e2e363885594..cc16c29c6c861 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -2814,6 +2814,8 @@ 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, using_cow=using_copy_on_write())
         return self._constructor_from_mgr(new_mgr, axes=new_mgr.axes).__finalize__(
             self, method="round"
diff --git a/pandas/tests/series/methods/test_round.py b/pandas/tests/series/methods/test_round.py
index c330b7a7dfbbb..a78f77e990ae1 100644
--- a/pandas/tests/series/methods/test_round.py
+++ b/pandas/tests/series/methods/test_round.py
@@ -72,3 +72,10 @@ def test_round_ea_boolean(self):
         tm.assert_series_equal(result, expected)
         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."
+        with pytest.raises(TypeError, match=msg):
+            ser.round()