diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 8d3ac0e396430..4402ae0f860ea 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -73,6 +73,7 @@ Other enhancements
 - :meth:`.DataFrameGroupBy.transform`, :meth:`.SeriesGroupBy.transform`, :meth:`.DataFrameGroupBy.agg`, :meth:`.SeriesGroupBy.agg`, :meth:`.SeriesGroupBy.apply`, :meth:`.DataFrameGroupBy.apply` now support ``kurt`` (:issue:`40139`)
 - :meth:`DataFrame.apply` supports using third-party execution engines like the Bodo.ai JIT compiler (:issue:`60668`)
 - :meth:`DataFrame.iloc` and :meth:`Series.iloc` now support boolean masks in ``__getitem__`` for more consistent indexing behavior (:issue:`60994`)
+- :meth:`DataFrame.round` now raises a ``Type Error`` if any columns are non-numeric (:issue:`61679`)
 - :meth:`DataFrameGroupBy.transform`, :meth:`SeriesGroupBy.transform`, :meth:`DataFrameGroupBy.agg`, :meth:`SeriesGroupBy.agg`, :meth:`RollingGroupby.apply`, :meth:`ExpandingGroupby.apply`, :meth:`Rolling.apply`, :meth:`Expanding.apply`, :meth:`DataFrame.apply` with ``engine="numba"`` now supports positional arguments passed as kwargs (:issue:`58995`)
 - :meth:`Rolling.agg`, :meth:`Expanding.agg` and :meth:`ExponentialMovingWindow.agg` now accept :class:`NamedAgg` aggregations through ``**kwargs`` (:issue:`28333`)
 - :meth:`Series.map` can now accept kwargs to pass on to func (:issue:`59814`)
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 8053c17437c5e..70569fc687a8e 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -11152,7 +11152,7 @@ def round(
         Returns
         -------
         DataFrame
-            A DataFrame with the affected columns rounded to the specified
+            A DataFrame with columns rounded to the specified
             number of decimal places.
 
         See Also
@@ -11227,7 +11227,10 @@ def _series_round(ser: Series, decimals: int) -> Series:
             return ser
 
         nv.validate_round(args, kwargs)
-
+        if "object" in self.dtypes.values:
+            raise TypeError(
+                "All columns must be numeric dtype, but got object dtype column"
+            )
         if isinstance(decimals, (dict, Series)):
             if isinstance(decimals, Series) and not decimals.index.is_unique:
                 raise ValueError("Index of decimals must be unique")
diff --git a/pandas/tests/copy_view/test_methods.py b/pandas/tests/copy_view/test_methods.py
index 250697c91ff13..1e0d98b51134f 100644
--- a/pandas/tests/copy_view/test_methods.py
+++ b/pandas/tests/copy_view/test_methods.py
@@ -911,11 +911,11 @@ def test_sort_values_inplace(obj, kwargs):
 
 @pytest.mark.parametrize("decimals", [-1, 0, 1])
 def test_round(decimals):
-    df = DataFrame({"a": [1, 2], "b": "c"})
+    df = DataFrame({"a": [1, 2], "b": [3.3, 4.4]})
     df_orig = df.copy()
     df2 = df.round(decimals=decimals)
 
-    assert tm.shares_memory(get_array(df2, "b"), get_array(df, "b"))
+    assert not tm.shares_memory(get_array(df2, "b"), get_array(df, "b"))
     # TODO: Make inplace by using out parameter of ndarray.round?
     if decimals >= 0:
         # Ensure lazy copy if no-op
@@ -923,8 +923,8 @@ def test_round(decimals):
     else:
         assert not np.shares_memory(get_array(df2, "a"), get_array(df, "a"))
 
-    df2.iloc[0, 1] = "d"
-    df2.iloc[0, 0] = 4
+    df2.iloc[0, 1] = 6.6
+    df2.iloc[0, 0] = 5
     assert not np.shares_memory(get_array(df2, "b"), get_array(df, "b"))
     assert not np.shares_memory(get_array(df2, "a"), get_array(df, "a"))
     tm.assert_frame_equal(df, df_orig)
diff --git a/pandas/tests/frame/methods/test_round.py b/pandas/tests/frame/methods/test_round.py
index a96df27b48d7d..b09d4f8dbbfc4 100644
--- a/pandas/tests/frame/methods/test_round.py
+++ b/pandas/tests/frame/methods/test_round.py
@@ -5,7 +5,6 @@
 from pandas import (
     DataFrame,
     Series,
-    date_range,
 )
 import pandas._testing as tm
 
@@ -143,29 +142,6 @@ def test_round_numpy_with_nan(self):
         expected = Series([2.0, np.nan, 0.0]).to_frame()
         tm.assert_frame_equal(result, expected)
 
-    def test_round_mixed_type(self):
-        # GH#11885
-        df = DataFrame(
-            {
-                "col1": [1.1, 2.2, 3.3, 4.4],
-                "col2": ["1", "a", "c", "f"],
-                "col3": date_range("20111111", periods=4),
-            }
-        )
-        round_0 = DataFrame(
-            {
-                "col1": [1.0, 2.0, 3.0, 4.0],
-                "col2": ["1", "a", "c", "f"],
-                "col3": date_range("20111111", periods=4),
-            }
-        )
-        tm.assert_frame_equal(df.round(), round_0)
-        tm.assert_frame_equal(df.round(1), df)
-        tm.assert_frame_equal(df.round({"col1": 1}), df)
-        tm.assert_frame_equal(df.round({"col1": 0}), round_0)
-        tm.assert_frame_equal(df.round({"col1": 0, "col2": 1}), round_0)
-        tm.assert_frame_equal(df.round({"col3": 1}), df)
-
     def test_round_with_duplicate_columns(self):
         # GH#11611
 
@@ -223,3 +199,10 @@ def test_round_empty_not_input(self):
         result = df.round()
         tm.assert_frame_equal(df, result)
         assert df is not result
+
+    def test_round_non_numeric_columns(self):
+        # GH#61679
+        df = DataFrame({"col1": [1.22, 10.32, 3.54], "col2": ["a", "b", "c"]})
+        msg = "All columns must be numeric dtype, but got object dtype column"
+        with pytest.raises(TypeError, match=msg):
+            df.round()