diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 837bd35414773..606bd4cc3b52d 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -8647,13 +8647,11 @@ def blk_func(values):
                     return op(values, axis=1, skipna=skipna, **kwds)
 
             # After possibly _get_data and transposing, we are now in the
-            #  simple case where we can use BlockManager._reduce
+            #  simple case where we can use BlockManager.reduce
             res = df._mgr.reduce(blk_func)
-            assert isinstance(res, dict)
-            if len(res):
-                assert len(res) == max(list(res.keys())) + 1, res.keys()
-            out = df._constructor_sliced(res, index=range(len(res)), dtype=out_dtype)
-            out.index = df.columns
+            out = df._constructor(res,).iloc[0].rename(None)
+            if out_dtype is not None:
+                out = out.astype(out_dtype)
             if axis == 0 and is_object_dtype(out.dtype):
                 out[:] = coerce_to_dtypes(out.values, df.dtypes)
             return out
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index f3286b3c20965..c62be4f767f00 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -346,6 +346,21 @@ def apply(self, func, **kwargs) -> List["Block"]:
 
         return self._split_op_result(result)
 
+    def reduce(self, func) -> List["Block"]:
+        # We will apply the function and reshape the result into a single-row
+        #  Block with the same mgr_locs; squeezing will be done at a higher level
+        assert self.ndim == 2
+
+        result = func(self.values)
+        if np.ndim(result) == 0:
+            # TODO(EA2D): special case not needed with 2D EAs
+            res_values = np.array([[result]])
+        else:
+            res_values = result.reshape(-1, 1)
+
+        nb = self.make_block(res_values)
+        return [nb]
+
     def _split_op_result(self, result) -> List["Block"]:
         # See also: split_and_operate
         if is_extension_array_dtype(result) and result.ndim > 1:
diff --git a/pandas/core/internals/managers.py b/pandas/core/internals/managers.py
index f05d4cf1c4be6..297ad3077ef1d 100644
--- a/pandas/core/internals/managers.py
+++ b/pandas/core/internals/managers.py
@@ -330,31 +330,18 @@ def _verify_integrity(self) -> None:
                 f"tot_items: {tot_items}"
             )
 
-    def reduce(self, func):
+    def reduce(self: T, func) -> T:
         # If 2D, we assume that we're operating column-wise
-        if self.ndim == 1:
-            # we'll be returning a scalar
-            blk = self.blocks[0]
-            return func(blk.values)
+        assert self.ndim == 2
 
-        res = {}
+        res_blocks = []
         for blk in self.blocks:
-            bres = func(blk.values)
-
-            if np.ndim(bres) == 0:
-                # EA
-                assert blk.shape[0] == 1
-                new_res = zip(blk.mgr_locs.as_array, [bres])
-            else:
-                assert bres.ndim == 1, bres.shape
-                assert blk.shape[0] == len(bres), (blk.shape, bres.shape)
-                new_res = zip(blk.mgr_locs.as_array, bres)
-
-            nr = dict(new_res)
-            assert not any(key in res for key in nr)
-            res.update(nr)
+            nbs = blk.reduce(func)
+            res_blocks.extend(nbs)
 
-        return res
+        index = Index([0])  # placeholder
+        new_mgr = BlockManager.from_blocks(res_blocks, [self.items, index])
+        return new_mgr
 
     def operate_blockwise(self, other: "BlockManager", array_op) -> "BlockManager":
         """