diff --git a/pandas/core/apply.py b/pandas/core/apply.py
index 3a2c2d7124963..cb20f6c69e6f1 100644
--- a/pandas/core/apply.py
+++ b/pandas/core/apply.py
@@ -633,25 +633,18 @@ def agg(self):
         obj = self.obj
         axis = self.axis
 
-        try:
-            if axis == 1:
-                result = FrameRowApply(
-                    obj.T,
-                    self.orig_f,
-                    self.raw,
-                    self.result_type,
-                    self.args,
-                    self.kwargs,
-                ).agg()
-                result = result.T if result is not None else result
-            else:
-                result = super().agg()
-        except TypeError as err:
-            exc = TypeError(
-                "DataFrame constructor called with "
-                f"incompatible data and dtype: {err}"
-            )
-            raise exc from err
+        if axis == 1:
+            result = FrameRowApply(
+                obj.T,
+                self.orig_f,
+                self.raw,
+                self.result_type,
+                self.args,
+                self.kwargs,
+            ).agg()
+            result = result.T if result is not None else result
+        else:
+            result = super().agg()
 
         if result is None:
             result = obj.apply(self.orig_f, axis, args=self.args, **self.kwargs)
diff --git a/pandas/tests/apply/test_invalid_arg.py b/pandas/tests/apply/test_invalid_arg.py
index 690d6bed0cb9b..73bc5b14335d4 100644
--- a/pandas/tests/apply/test_invalid_arg.py
+++ b/pandas/tests/apply/test_invalid_arg.py
@@ -272,6 +272,14 @@ def test_agg_cython_table_raises_series(series, func, expected):
         series.agg(func)
 
 
+def test_agg_none_to_type():
+    # GH 40543
+    df = DataFrame({"a": [None]})
+    msg = re.escape("int() argument must be a string")
+    with pytest.raises(TypeError, match=msg):
+        df.agg({"a": int})
+
+
 def test_transform_none_to_type():
     # GH#34377
     df = DataFrame({"a": [None]})