diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 84ad478226175..58aab96aa95eb 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -784,6 +784,7 @@ Reshaping
 - Bug in :func:`concat` was not allowing for concatenation of ``DataFrame`` and ``Series`` with duplicate keys (:issue:`33654`)
 - Bug in :func:`cut` raised an error when non-unique labels (:issue:`33141`)
 - Bug in :meth:`DataFrame.replace` casts columns to ``object`` dtype if items in ``to_replace`` not in values (:issue:`32988`)
+- Ensure only named functions can be used in :func:`eval()` (:issue:`32460`)
 
 
 Sparse
diff --git a/pandas/core/computation/expr.py b/pandas/core/computation/expr.py
index 6cd9a15b70d39..fcccc24ed7615 100644
--- a/pandas/core/computation/expr.py
+++ b/pandas/core/computation/expr.py
@@ -641,7 +641,7 @@ def visit_Attribute(self, node, **kwargs):
 
     def visit_Call(self, node, side=None, **kwargs):
 
-        if isinstance(node.func, ast.Attribute):
+        if isinstance(node.func, ast.Attribute) and node.func.attr != "__call__":
             res = self.visit_Attribute(node.func)
         elif not isinstance(node.func, ast.Name):
             raise TypeError("Only named functions are supported")
diff --git a/pandas/tests/frame/test_query_eval.py b/pandas/tests/frame/test_query_eval.py
index 1a07780462ea3..8612c05e6a996 100644
--- a/pandas/tests/frame/test_query_eval.py
+++ b/pandas/tests/frame/test_query_eval.py
@@ -1181,3 +1181,24 @@ def test_failing_character_outside_range(self, df):
     def test_failing_hashtag(self, df):
         with pytest.raises(SyntaxError):
             df.query("`foo#bar` > 4")
+
+    def test_call_non_named_expression(self, df):
+        """
+        Only attributes and variables ('named functions') can be called.
+        .__call__() is not an allowed attribute because that would allow
+        calling anything.
+        https://github.com/pandas-dev/pandas/pull/32460
+        """
+
+        def func(*_):
+            return 1
+
+        funcs = [func]  # noqa
+
+        df.eval("@func()")
+
+        with pytest.raises(TypeError, match="Only named functions are supported"):
+            df.eval("@funcs[0]()")
+
+        with pytest.raises(TypeError, match="Only named functions are supported"):
+            df.eval("@funcs[0].__call__()")