diff --git a/core/string.rbs b/core/string.rbs
index 6c603af75..e6e9b6ed0 100644
--- a/core/string.rbs
+++ b/core/string.rbs
@@ -2733,8 +2733,8 @@ class String
   #     <<cruel>> <<world>>
   #     rceu lowlr
   #
-  def scan: (Regexp pattern) -> Array[String | Array[String]]
-          | (Regexp pattern) { (String | Array[String] matches) -> void } -> self
+  def scan: (Regexp pattern) -> Array[String | Array[String?]]
+          | (Regexp pattern) { (String | Array[String?] matches) -> void } -> self
           | (string pattern) -> Array[String]
           | (string pattern) { (String match) -> void } -> self
 
diff --git a/test/stdlib/String_test.rb b/test/stdlib/String_test.rb
index e6429a41a..60795707c 100644
--- a/test/stdlib/String_test.rb
+++ b/test/stdlib/String_test.rb
@@ -1259,11 +1259,15 @@ def test_scan
                       'hello', :scan, /l/
     assert_send_type  '(Regexp) -> Array[Array[String]]',
                       'hello', :scan, /(l)/
+    assert_send_type  '(Regexp) -> Array[Array[nil]]',
+                      'hello', :scan, /(x)?/
 
     assert_send_type  '(Regexp) { (String) -> void } -> String',
                       'hello', :scan, /l/ do end
     assert_send_type  '(Regexp) { (Array[String]) -> void } -> String',
                       'hello', :scan, /(l)/ do end
+    assert_send_type  '(Regexp) { (Array[nil]) -> void } -> String',
+                      'hello', :scan, /(x)?/ do end
 
     with_string 'l' do |pattern|
       assert_send_type  '(string) -> Array[String]',