diff --git a/Library/Homebrew/rubocops/cask/array_alphabetization.rb b/Library/Homebrew/rubocops/cask/array_alphabetization.rb
index 335a5e22c2..2b0766b47b 100644
--- a/Library/Homebrew/rubocops/cask/array_alphabetization.rb
+++ b/Library/Homebrew/rubocops/cask/array_alphabetization.rb
@@ -7,18 +7,19 @@ module RuboCop
       class ArrayAlphabetization < Base
         extend AutoCorrector
 
-        SINGLE_MSG = "Remove the `[]` around a single `zap trash` path".freeze
-        NON_ALPHABETICAL_MSG = "The `zap trash` paths should be in alphabetical order".freeze
-
         def on_send(node)
-          return if node.method_name != :zap
+          return unless [:zap, :uninstall].include?(name = node.method_name)
 
           node.each_descendant(:pair).each do |pair|
-            next if pair.children.select(&:sym_type?).map(&:value) != [:trash]
+            symbols = pair.children.select { |child| child.sym_type? }.map(&:value)
+            # For `zap`s, we only care about `trash` arrays.
+            next if name == :zap && !symbols.include?(:trash)
+            # Don't order `uninstall` arrays that contain commands.
+            next if name == :uninstall && (symbols & [:signal, :script, :early_script]).any?
 
             pair.each_descendant(:array).each do |array|
               if array.children.length == 1
-                add_offense(array, message: SINGLE_MSG) do |corrector|
+                add_offense(array, message: "Avoid single-element arrays by removing the []") do |corrector|
                   corrector.replace(array.source_range, array.children.first.source)
                 end
               end
@@ -28,7 +29,7 @@ module RuboCop
               sorted_array = array.children.sort_by { |child| child.source.downcase }
               next if sorted_array.map(&:source) == array.children.map(&:source)
 
-              add_offense(array, message: NON_ALPHABETICAL_MSG) do |corrector|
+              add_offense(array, message: "The array elements should be ordered alphabetically") do |corrector|
                 array.children.each_with_index do |child, index|
                   corrector.replace(child.source_range, sorted_array[index].source)
                 end
diff --git a/Library/Homebrew/test/rubocops/cask/array_alphabetization_spec.rb b/Library/Homebrew/test/rubocops/cask/array_alphabetization_spec.rb
index 73f79a2e6e..d576ef9573 100644
--- a/Library/Homebrew/test/rubocops/cask/array_alphabetization_spec.rb
+++ b/Library/Homebrew/test/rubocops/cask/array_alphabetization_spec.rb
@@ -9,7 +9,7 @@ describe RuboCop::Cop::Cask::ArrayAlphabetization, :config do
         url "https://example.com/foo.zip"
 
         zap trash: ["~/Library/Application Support/Foo"]
-                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Remove the `[]` around a single `zap trash` path
+                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Avoid single-element arrays by removing the []
       end
     CASK
 
@@ -28,7 +28,7 @@ describe RuboCop::Cop::Cask::ArrayAlphabetization, :config do
         url "https://example.com/foo.zip"
 
         zap trash: [
-                   ^ The `zap trash` paths should be in alphabetical order
+                   ^ The array elements should be ordered alphabetically
           "/Library/Application Support/Foo",
           "/Library/Application Support/Baz",
           "~/Library/Application Support/Foo",
@@ -59,7 +59,7 @@ describe RuboCop::Cop::Cask::ArrayAlphabetization, :config do
         url "https://example.com/foo.zip"
 
         zap trash: [
-                   ^ The `zap trash` paths should be in alphabetical order
+                   ^ The array elements should be ordered alphabetically
           "~/Library/Application Support/Foo",
           "~/Library/Application Support/Bar\#{version.major}",
         ]
@@ -90,4 +90,37 @@ describe RuboCop::Cop::Cask::ArrayAlphabetization, :config do
       end
     CASK
   end
+
+  it "autocorrects alphabetization in `uninstall` methods" do
+    expect_offense(<<~CASK)
+      cask "foo" do
+        url "https://example.com/foo.zip"
+
+        uninstall pkgutil: [
+                           ^ The array elements should be ordered alphabetically
+          "something",
+          "other",
+        ],
+        script: [
+          "ordered",
+          "differently",
+        ]
+      end
+    CASK
+
+    expect_correction(<<~CASK)
+      cask "foo" do
+        url "https://example.com/foo.zip"
+
+        uninstall pkgutil: [
+          "other",
+          "something",
+        ],
+        script: [
+          "ordered",
+          "differently",
+        ]
+      end
+    CASK
+  end
 end