diff --git a/CHANGELOG.md b/CHANGELOG.md
index 7142d2aff43..41930d37057 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -16,6 +16,7 @@
 * [#7641](https://github.com/rubocop-hq/rubocop/issues/7641): **(Breaking)** Remove `Style/BracesAroundHashParameters` cop. ([@pocke][])
 * Add the method name to highlight area of `Layout/EmptyLineBetweenDefs` to help provide more context. ([@rrosenblum][])
 * [#7652](https://github.com/rubocop-hq/rubocop/pull/7652): Allow `pp` to allowed names of `Naming/MethodParameterName` cop in default config. ([@masarakki][])
+* [#7331](https://github.com/rubocop-hq/rubocop/issues/7331): Add `forbidden` option to `Style/ModuleFunction` cop. ([@weh][])
 
 ## 0.79.0 (2020-01-06)
 
diff --git a/config/default.yml b/config/default.yml
index f83c62bd6b9..06bb2612fb2 100644
--- a/config/default.yml
+++ b/config/default.yml
@@ -3038,6 +3038,7 @@ Style/ModuleFunction:
   SupportedStyles:
     - module_function
     - extend_self
+    - forbidden
   Autocorrect: false
   SafeAutoCorrect: false
 
diff --git a/lib/rubocop/cop/style/module_function.rb b/lib/rubocop/cop/style/module_function.rb
index 5811100a9cf..401d1ab8532 100644
--- a/lib/rubocop/cop/style/module_function.rb
+++ b/lib/rubocop/cop/style/module_function.rb
@@ -6,7 +6,7 @@ module Style
       # This cop checks for use of `extend self` or `module_function` in a
       # module.
       #
-      # Supported styles are: module_function, extend_self.
+      # Supported styles are: module_function, extend_self, forbidden.
       #
       # @example EnforcedStyle: module_function (default)
       #   # bad
@@ -46,6 +46,29 @@ module Style
       #     # ...
       #   end
       #
+      # The option `forbidden` prohibits the usage of both styles.
+      #
+      # @example EnforcedStyle: forbidden
+      #   # bad
+      #   module Test
+      #     module_function
+      #     # ...
+      #   end
+      #
+      #   # bad
+      #   module Test
+      #     extend self
+      #     # ...
+      #   end
+      #
+      #   # bad
+      #   module Test
+      #     extend self
+      #     # ...
+      #     private
+      #     # ...
+      #   end
+      #
       # These offenses are not safe to auto-correct since there are different
       # implications to each approach.
       class ModuleFunction < Cop
@@ -55,6 +78,8 @@ class ModuleFunction < Cop
           'Use `module_function` instead of `extend self`.'
         EXTEND_SELF_MSG =
           'Use `extend self` instead of `module_function`.'
+        FORBIDDEN_MSG =
+          'Do not use `module_function` or `extend self`.'
 
         def_node_matcher :module_function_node?, '(send nil? :module_function)'
         def_node_matcher :extend_self_node?, '(send nil? :extend self)'
@@ -69,6 +94,8 @@ def on_module(node)
         end
 
         def autocorrect(node)
+          return if style == :forbidden
+
           lambda do |corrector|
             if extend_self_node?(node)
               corrector.replace(node.source_range, 'module_function')
@@ -80,22 +107,41 @@ def autocorrect(node)
 
         private
 
-        def each_wrong_style(nodes)
+        def each_wrong_style(nodes, &block)
           case style
           when :module_function
-            private_directive = nodes.any? { |node| private_directive?(node) }
-
-            nodes.each do |node|
-              yield node if extend_self_node?(node) && !private_directive
-            end
+            check_module_function(nodes, &block)
           when :extend_self
-            nodes.each do |node|
-              yield node if module_function_node?(node)
-            end
+            check_extend_self(nodes, &block)
+          when :forbidden
+            check_forbidden(nodes, &block)
+          end
+        end
+
+        def check_module_function(nodes)
+          private_directive = nodes.any? { |node| private_directive?(node) }
+
+          nodes.each do |node|
+            yield node if extend_self_node?(node) && !private_directive
+          end
+        end
+
+        def check_extend_self(nodes)
+          nodes.each do |node|
+            yield node if module_function_node?(node)
+          end
+        end
+
+        def check_forbidden(nodes)
+          nodes.each do |node|
+            yield node if extend_self_node?(node)
+            yield node if module_function_node?(node)
           end
         end
 
         def message(_node)
+          return FORBIDDEN_MSG if style == :forbidden
+
           style == :module_function ? MODULE_FUNCTION_MSG : EXTEND_SELF_MSG
         end
       end
diff --git a/manual/cops_style.md b/manual/cops_style.md
index 9821432bcf9..4d75b9e04cf 100644
--- a/manual/cops_style.md
+++ b/manual/cops_style.md
@@ -3616,11 +3616,13 @@ Enabled | Yes | Yes (Unsafe) | 0.11 | 0.65
 This cop checks for use of `extend self` or `module_function` in a
 module.
 
-Supported styles are: module_function, extend_self.
+Supported styles are: module_function, extend_self, forbidden.
 
 In case there are private methods, the cop won't be activated.
 Otherwise, it forces to change the flow of the default code.
 
+The option `forbidden` prohibits the usage of both styles.
+
 These offenses are not safe to auto-correct since there are different
 implications to each approach.
 
@@ -3667,12 +3669,35 @@ module Test
   # ...
 end
 ```
+#### EnforcedStyle: forbidden
+
+```ruby
+# bad
+module Test
+  module_function
+  # ...
+end
+
+# bad
+module Test
+  extend self
+  # ...
+end
+
+# bad
+module Test
+  extend self
+  # ...
+  private
+  # ...
+end
+```
 
 ### Configurable attributes
 
 Name | Default value | Configurable values
 --- | --- | ---
-EnforcedStyle | `module_function` | `module_function`, `extend_self`
+EnforcedStyle | `module_function` | `module_function`, `extend_self`, `forbidden`
 Autocorrect | `false` | Boolean
 
 ### References
diff --git a/spec/rubocop/cop/style/module_function_spec.rb b/spec/rubocop/cop/style/module_function_spec.rb
index 8eab6d4f1ab..5409f4606de 100644
--- a/spec/rubocop/cop/style/module_function_spec.rb
+++ b/spec/rubocop/cop/style/module_function_spec.rb
@@ -82,4 +82,69 @@ def test; end
       RUBY
     end
   end
+
+  context 'when enforced style is `forbidden`' do
+    let(:cop_config) { { 'EnforcedStyle' => 'forbidden' } }
+
+    context 'registers an offense for `extend self`' do
+      it 'in a module' do
+        expect_offense(<<~RUBY)
+          module Test
+            extend self
+            ^^^^^^^^^^^ Do not use `module_function` or `extend self`.
+            def test; end
+          end
+        RUBY
+
+        expect_no_corrections
+      end
+
+      it 'in a module with private methods' do
+        expect_offense(<<~RUBY)
+          module Test
+            extend self
+            ^^^^^^^^^^^ Do not use `module_function` or `extend self`.
+            def test; end
+            private
+            def test_private;end
+          end
+        RUBY
+
+        expect_no_corrections
+      end
+
+      it 'in a module with declarative private' do
+        expect_offense(<<~RUBY)
+          module Test
+            extend self
+            ^^^^^^^^^^^ Do not use `module_function` or `extend self`.
+            def test; end
+            private :test
+          end
+        RUBY
+
+        expect_no_corrections
+      end
+    end
+
+    it 'accepts `extend self` in a class' do
+      expect_no_offenses(<<~RUBY)
+        class Test
+          extend self
+        end
+      RUBY
+    end
+
+    it 'registers an offense for `module_function` without an argument' do
+      expect_offense(<<~RUBY)
+        module Test
+          module_function
+          ^^^^^^^^^^^^^^^ Do not use `module_function` or `extend self`.
+          def test; end
+        end
+      RUBY
+
+      expect_no_corrections
+    end
+  end
 end