diff --git a/scripts/release/homebrew/docker/formula_generate.py b/scripts/release/homebrew/docker/formula_generate.py
index 590c2229fa9..52139fdd380 100644
--- a/scripts/release/homebrew/docker/formula_generate.py
+++ b/scripts/release/homebrew/docker/formula_generate.py
@@ -71,6 +71,12 @@ def compute_sha256(resource_url: str) -> str:
 
 def collect_resources() -> str:
     nodes = make_graph('azure-cli')
+    # `Pygments`, `PyYAML`, `six`, and `typing-extensions` are provided by separate Homebrew packages,
+    # and so should not be included in the resources section
+    already_packaged = ["Pygments", "PyYAML", "six", "typing-extensions"]
+    for package_name in already_packaged:
+        del nodes[package_name]
+
     nodes_render = []
     for node_name in sorted(nodes):
         if not resource_filter(node_name):
diff --git a/scripts/release/homebrew/docker/formula_template.txt b/scripts/release/homebrew/docker/formula_template.txt
index bf1c58c6a2f..4b4ec0c87ce 100644
--- a/scripts/release/homebrew/docker/formula_template.txt
+++ b/scripts/release/homebrew/docker/formula_template.txt
@@ -17,7 +17,11 @@ class AzureCli < Formula
 {{ bottle_hash }}
 
   depends_on "openssl@1.1"
+  depends_on "pygments"
+  depends_on "python-typing-extensions"
   depends_on "python@3.10"
+  depends_on "pyyaml"
+  depends_on "six"
 
   uses_from_macos "libffi"