diff --git a/Library/Homebrew/rubocops/cask/no_overrides.rb b/Library/Homebrew/rubocops/cask/no_overrides.rb
index 6dafc294b0..a7a65c751f 100644
--- a/Library/Homebrew/rubocops/cask/no_overrides.rb
+++ b/Library/Homebrew/rubocops/cask/no_overrides.rb
@@ -43,7 +43,9 @@ module RuboCop
                 # Skip (nested) livecheck blocks as its `url` is different to a download `url`.
                 next if send_node.method_name == :livecheck || inside_livecheck_block?(send_node)
                 # Skip string interpolations.
-                next if send_node.ancestors.drop_while { |a| !a.begin_type? }.any?(&:dstr_type?)
+                if send_node.ancestors.drop_while { |a| !a.begin_type? }.any? { |a| a.dstr_type? || a.regexp_type? }
+                  next
+                end
                 next if ON_SYSTEM_METHODS.include?(send_node.method_name)
 
                 names.add(send_node.method_name)
diff --git a/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb b/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb
index d7b43cf0a1..312035d140 100644
--- a/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb
+++ b/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb
@@ -71,6 +71,29 @@ describe RuboCop::Cop::Cask::NoOverrides do
     include_examples "does not report any offenses"
   end
 
+  context "when there are `arch` interpolations in regexps in `on_*` blocks" do
+    let(:source) do
+      <<~CASK
+        cask 'foo' do
+          arch arm: "arm64", intel: "x86"
+
+          version 0.99,123.3
+
+          on_mojave :or_later do
+            url "https://brew.sh/foo-\#{arch}-\#{version.csv.first}-\#{version.csv.last}.pkg"
+
+            livecheck do
+              url "https://brew.sh/foo/releases.html"
+              regex(/href=.*?foo[._-]v?(\d+(?:.\d+)+)-\#{arch}.pkg/i)
+            end
+          end
+        end
+      CASK
+    end
+
+    include_examples "does not report any offenses"
+  end
+
   context "when there are single-line livecheck blocks within `on_*` blocks, ignore their contents" do
     let(:source) do
       <<~CASK