diff --git a/sphinx/ext/autodoc/__init__.py b/sphinx/ext/autodoc/__init__.py
index 3eeec4523..5b260c6fe 100644
--- a/sphinx/ext/autodoc/__init__.py
+++ b/sphinx/ext/autodoc/__init__.py
@@ -993,7 +993,9 @@ class FunctionDocumenter(DocstringSignatureMixin, ModuleLevelDocumenter):  # typ
     @classmethod
     def can_document_member(cls, member, membername, isattr, parent):
         # type: (Any, str, bool, Any) -> bool
-        return inspect.isfunction(member) or inspect.isbuiltin(member)
+        # supports functions, builtins and bound methods exported at the module level
+        return (inspect.isfunction(member) or inspect.isbuiltin(member) or
+                (inspect.isroutine(member) and isinstance(parent, ModuleDocumenter)))
 
     def format_args(self):
         # type: () -> str
diff --git a/tests/roots/test-ext-autodoc/target/bound_method.py b/tests/roots/test-ext-autodoc/target/bound_method.py
new file mode 100644
index 000000000..d48b9ee1c
--- /dev/null
+++ b/tests/roots/test-ext-autodoc/target/bound_method.py
@@ -0,0 +1,7 @@
+class Cls:
+    def method(self):
+        """Method docstring"""
+        pass
+
+
+bound_method = Cls().method
diff --git a/tests/test_autodoc.py b/tests/test_autodoc.py
index 27412a9da..07e82b54a 100644
--- a/tests/test_autodoc.py
+++ b/tests/test_autodoc.py
@@ -259,6 +259,11 @@ def test_format_signature():
     assert formatsig('method', 'H.foo', H.foo2, None, None) == '(*c)'
     assert formatsig('method', 'H.foo', H.foo3, None, None) == r"(d='\\n')"
 
+    # test bound methods interpreted as functions
+    assert formatsig('function', 'foo', H().foo1, None, None) == '(b, *c)'
+    assert formatsig('function', 'foo', H().foo2, None, None) == '(*c)'
+    assert formatsig('function', 'foo', H().foo3, None, None) == r"(d='\\n')"
+
     # test exception handling (exception is caught and args is '')
     directive.env.config.autodoc_docstring_signature = False
     assert formatsig('function', 'int', int, None, None) == ''
@@ -451,6 +456,14 @@ def test_get_doc():
     directive.env.config.autoclass_content = 'both'
     assert getdocl('class', I) == ['Class docstring', '', 'New docstring']
 
+    # verify that method docstrings get extracted in both normal case
+    # and in case of bound method posing as a function
+    class J:  # NOQA
+        def foo(self):
+            """Method docstring"""
+    assert getdocl('method', J.foo) == ['Method docstring']
+    assert getdocl('function', J().foo) == ['Method docstring']
+
     from target import Base, Derived
 
     # NOTE: inspect.getdoc seems not to work with locally defined classes
@@ -1463,6 +1476,23 @@ def test_partialfunction():
     ]
 
 
+@pytest.mark.usefixtures('setup_test')
+def test_bound_method():
+    options = {"members": None}
+    actual = do_autodoc(app, 'module', 'target.bound_method', options)
+    assert list(actual) == [
+        '',
+        '.. py:module:: target.bound_method',
+        '',
+        '',
+        '.. py:function:: bound_method()',
+        '   :module: target.bound_method',
+        '',
+        '   Method docstring',
+        '   ',
+    ]
+
+
 @pytest.mark.usefixtures('setup_test')
 def test_coroutine():
     options = {"members": None}