diff --git a/modin/core/dataframe/pandas/utils.py b/modin/core/dataframe/pandas/utils.py
index bb8d018e6e2..c1703d6f2db 100644
--- a/modin/core/dataframe/pandas/utils.py
+++ b/modin/core/dataframe/pandas/utils.py
@@ -44,4 +44,8 @@ def concatenate(dfs):
                 i, pandas.Categorical(df.iloc[:, i], categories=union.categories)
             )
     # `ValueError: buffer source array is read-only` if copy==False
+    if len(dfs) == 1:
+        # concat doesn't make a copy if len(dfs) == 1,
+        # so do it explicitly
+        return dfs[0].copy()
     return pandas.concat(dfs, copy=True)
diff --git a/modin/pandas/test/test_general.py b/modin/pandas/test/test_general.py
index 2f6f331f4d4..2fec3371ca9 100644
--- a/modin/pandas/test/test_general.py
+++ b/modin/pandas/test/test_general.py
@@ -835,6 +835,36 @@ def test_to_pandas_indices(data):
         ), f"Levels of indices at axis {axis} are different!"
 
 
+def test_to_pandas_read_only_issue():
+    df = pd.DataFrame(
+        [
+            [np.nan, 2, np.nan, 0],
+            [3, 4, np.nan, 1],
+            [np.nan, np.nan, np.nan, np.nan],
+            [np.nan, 3, np.nan, 4],
+        ],
+        columns=list("ABCD"),
+    )
+    pdf = df._to_pandas()
+    # there shouldn't be `ValueError: putmask: output array is read-only`
+    pdf.fillna(0, inplace=True)
+
+
+def test_to_numpy_read_only_issue():
+    df = pd.DataFrame(
+        [
+            [np.nan, 2, np.nan, 0],
+            [3, 4, np.nan, 1],
+            [np.nan, np.nan, np.nan, np.nan],
+            [np.nan, 3, np.nan, 4],
+        ],
+        columns=list("ABCD"),
+    )
+    arr = df.to_numpy()
+    # there shouldn't be `ValueError: putmask: output array is read-only`
+    np.putmask(arr, np.isnan(arr), 0)
+
+
 def test_create_categorical_dataframe_with_duplicate_column_name():
     # This tests for https://github.com/modin-project/modin/issues/4312
     pd_df = pandas.DataFrame(