diff --git a/changelog/fix_a_false_positive_for_lint_out_of_range_regexp_ref.md b/changelog/fix_a_false_positive_for_lint_out_of_range_regexp_ref.md
new file mode 100644
index 00000000000..b67d128a49c
--- /dev/null
+++ b/changelog/fix_a_false_positive_for_lint_out_of_range_regexp_ref.md
@@ -0,0 +1 @@
+* [#10552](https://github.com/rubocop/rubocop/issues/10552): Require RuboCop AST 1.20.0+ to fix a false positive for `Lint/OutOfRangeRegexpRef` when using fixed-encoding regopt. ([@koic][])
diff --git a/rubocop.gemspec b/rubocop.gemspec
index d44afb44c90..0146ac7aaed 100644
--- a/rubocop.gemspec
+++ b/rubocop.gemspec
@@ -37,7 +37,7 @@ Gem::Specification.new do |s|
   s.add_runtime_dependency('rainbow', '>= 2.2.2', '< 4.0')
   s.add_runtime_dependency('regexp_parser', '>= 1.8', '< 3.0')
   s.add_runtime_dependency('rexml', '>= 3.2.5', '< 4.0')
-  s.add_runtime_dependency('rubocop-ast', '>= 1.19.1', '< 2.0')
+  s.add_runtime_dependency('rubocop-ast', '>= 1.20.0', '< 2.0')
   s.add_runtime_dependency('ruby-progressbar', '~> 1.7')
   s.add_runtime_dependency('unicode-display_width', '>= 1.4.0', '< 3.0')
 
diff --git a/spec/rubocop/cop/lint/out_of_range_regexp_ref_spec.rb b/spec/rubocop/cop/lint/out_of_range_regexp_ref_spec.rb
index f075eeecef3..32f9edc3c66 100644
--- a/spec/rubocop/cop/lint/out_of_range_regexp_ref_spec.rb
+++ b/spec/rubocop/cop/lint/out_of_range_regexp_ref_spec.rb
@@ -63,6 +63,14 @@
     RUBY
   end
 
+  it 'does not register offense to a regexp with encoding option and valid references for numbered captures' do
+    expect_no_offenses(<<~RUBY)
+      /(foo)(bar)/u =~ "foobar"
+      puts $1
+      puts $2
+    RUBY
+  end
+
   # RuboCop does not know a value of variables that it will contain in the regexp literal.
   # For example, `/(?<foo>#{var}*)` is interpreted as `/(?<foo>*)`.
   # So it does not offense when variables are used in regexp literals.