diff --git a/lib/irb/completion.rb b/lib/irb/completion.rb
index c7c0fb99e..385957c3f 100644
--- a/lib/irb/completion.rb
+++ b/lib/irb/completion.rb
@@ -296,7 +296,8 @@ def self.retrieve_completion_data(input, bind: IRB.conf[:MAIN_CONTEXT].workspace
           candidates.uniq!
         end
         if doc_namespace
-          "#{rec.class.name}#{sep}#{candidates.find{ |i| i == message }}"
+          rec_class = rec.is_a?(Module) ? rec : rec.class
+          "#{rec_class.name}#{sep}#{candidates.find{ |i| i == message }}"
         else
           select_message(receiver, message, candidates, sep)
         end
diff --git a/test/irb/test_completion.rb b/test/irb/test_completion.rb
index 260b8a889..c534301bc 100644
--- a/test/irb/test_completion.rb
+++ b/test/irb/test_completion.rb
@@ -86,8 +86,15 @@ def test_complete_require_relative
 
     def test_complete_variable
       str_example = ''
+      str_example.clear # suppress "assigned but unused variable" warning
       assert_include(IRB::InputCompletor.retrieve_completion_data("str_examp", bind: binding), "str_example")
       assert_equal(IRB::InputCompletor.retrieve_completion_data("str_example", bind: binding, doc_namespace: true), "String")
+      assert_equal(IRB::InputCompletor.retrieve_completion_data("str_example.to_s", bind: binding, doc_namespace: true), "String.to_s")
+    end
+
+    def test_complete_class_method
+      assert_include(IRB::InputCompletor.retrieve_completion_data("String.new", bind: binding), "String.new")
+      assert_equal(IRB::InputCompletor.retrieve_completion_data("String.new", bind: binding, doc_namespace: true), "String.new")
     end
   end
 end