diff --git a/Library/Homebrew/rubocops/lines.rb b/Library/Homebrew/rubocops/lines.rb
index 5f941a663e..dfbd45d529 100644
--- a/Library/Homebrew/rubocops/lines.rb
+++ b/Library/Homebrew/rubocops/lines.rb
@@ -211,6 +211,32 @@ module RuboCop
         end
       end
 
+      # This cop makes sure that formulae do not depend on `pyoxidizer` at build-time
+      # or run-time.
+      #
+      # @api private
+      class PyoxidizerCheck < FormulaCop
+        def audit_formula(_node, _class_node, _parent_class_node, body_node)
+          # Disallow use of PyOxidizer as a dependency in core
+          return unless formula_tap == "homebrew-core"
+
+          find_method_with_args(body_node, :depends_on, "pyoxidizer") do
+            problem "Formulae in homebrew/core should not use '#{@offensive_node.source}'."
+          end
+
+          [
+            :build,
+            [:build],
+            [:build, :test],
+            [:test, :build],
+          ].each do |type|
+            find_method_with_args(body_node, :depends_on, "pyoxidizer" => type) do
+              problem "Formulae in homebrew/core should not use '#{@offensive_node.source}'."
+            end
+          end
+        end
+      end
+
       # This cop makes sure that the safe versions of `popen_*` calls are used.
       #
       # @api private