diff --git a/doc/source/whatsnew/v1.2.4.rst b/doc/source/whatsnew/v1.2.4.rst
index 790ff4c78cad6..edf23bf89d7e1 100644
--- a/doc/source/whatsnew/v1.2.4.rst
+++ b/doc/source/whatsnew/v1.2.4.rst
@@ -15,7 +15,7 @@ including other versions of pandas.
 Fixed regressions
 ~~~~~~~~~~~~~~~~~
 
--
+- Fixed regression in :meth:`DataFrame.sum` when ``min_count`` greater than the :class:`DataFrame` shape was passed resulted in a ``ValueError`` (:issue:`39738`)
 -
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 0094ebc744a34..4c156d7470364 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -8786,6 +8786,7 @@ def _reduce(
         **kwds,
     ):
 
+        min_count = kwds.get("min_count", 0)
         assert filter_type is None or filter_type == "bool", filter_type
         out_dtype = "bool" if filter_type == "bool" else None
 
@@ -8830,7 +8831,7 @@ def _get_data() -> DataFrame:
                 data = self._get_bool_data()
             return data
 
-        if numeric_only is not None or axis == 0:
+        if (numeric_only is not None or axis == 0) and min_count == 0:
             # For numeric_only non-None and axis non-None, we know
             #  which blocks to use and no try/except is needed.
             #  For numeric_only=None only the case with axis==0 and no object
@@ -8847,7 +8848,7 @@ def _get_data() -> DataFrame:
 
             # After possibly _get_data and transposing, we are now in the
             #  simple case where we can use BlockManager.reduce
-            res, indexer = df._mgr.reduce(blk_func, ignore_failures=ignore_failures)
+            res, _ = df._mgr.reduce(blk_func, ignore_failures=ignore_failures)
             out = df._constructor(res).iloc[0]
             if out_dtype is not None:
                 out = out.astype(out_dtype)
@@ -8875,14 +8876,15 @@ def _get_data() -> DataFrame:
             with np.errstate(all="ignore"):
                 result = func(values)
 
-        if filter_type == "bool" and notna(result).all():
-            result = result.astype(np.bool_)
-        elif filter_type is None and is_object_dtype(result.dtype):
-            try:
-                result = result.astype(np.float64)
-            except (ValueError, TypeError):
-                # try to coerce to the original dtypes item by item if we can
-                pass
+        if hasattr(result, "dtype"):
+            if filter_type == "bool" and notna(result).all():
+                result = result.astype(np.bool_)
+            elif filter_type is None and is_object_dtype(result.dtype):
+                try:
+                    result = result.astype(np.float64)
+                except (ValueError, TypeError):
+                    # try to coerce to the original dtypes item by item if we can
+                    pass
 
         result = self._constructor_sliced(result, index=labels)
         return result
diff --git a/pandas/core/nanops.py b/pandas/core/nanops.py
index 88662a4fabed8..edc1b1e96509e 100644
--- a/pandas/core/nanops.py
+++ b/pandas/core/nanops.py
@@ -1,3 +1,5 @@
+from __future__ import annotations
+
 import functools
 import itertools
 import operator
@@ -1368,7 +1370,7 @@ def _maybe_null_out(
     mask: Optional[np.ndarray],
     shape: Tuple[int, ...],
     min_count: int = 1,
-) -> float:
+) -> Union[np.ndarray, float]:
     """
     Returns
     -------
diff --git a/pandas/tests/frame/test_reductions.py b/pandas/tests/frame/test_reductions.py
index d843d4b0e9504..cb481613eb97f 100644
--- a/pandas/tests/frame/test_reductions.py
+++ b/pandas/tests/frame/test_reductions.py
@@ -835,6 +835,13 @@ def test_sum_nanops_timedelta(self):
         expected = Series([0, 0, np.nan], dtype="m8[ns]", index=idx)
         tm.assert_series_equal(result, expected)
 
+    def test_sum_nanops_min_count(self):
+        # https://github.com/pandas-dev/pandas/issues/39738
+        df = DataFrame({"x": [1, 2, 3], "y": [4, 5, 6]})
+        result = df.sum(min_count=10)
+        expected = Series([np.nan, np.nan], index=["x", "y"])
+        tm.assert_series_equal(result, expected)
+
     def test_sum_object(self, float_frame):
         values = float_frame.values.astype(int)
         frame = DataFrame(values, index=float_frame.index, columns=float_frame.columns)