diff --git a/dev/tasks/macros.jinja b/dev/tasks/macros.jinja
index 72f575a1885..9cb0c0f8a84 100644
--- a/dev/tasks/macros.jinja
+++ b/dev/tasks/macros.jinja
@@ -235,6 +235,10 @@ on:
       brew unlink python@2 || true
       brew config
       brew doctor || true
+      # The GHA runners install of python > 3.10 is incompatible with brew so we
+      # have to force overwritting of the symlinks
+      # see https://github.com/actions/runner-images/issues/6868
+      brew install --overwrite python@3.11 python@3.10
 
       ARROW_GLIB_FORMULA=$(echo ${ARROW_FORMULA} | sed -e 's/\.rb/-glib.rb/')
       echo "ARROW_GLIB_FORMULA=${ARROW_GLIB_FORMULA}" >> ${GITHUB_ENV}
@@ -396,3 +400,4 @@ on:
   {{ key }}: "{{ value }}"
   {% endfor %}
 {% endmacro %}
+
diff --git a/dev/tasks/r/github.macos.brew.yml b/dev/tasks/r/github.macos.brew.yml
index 5f426ab42ce..7cf86d999db 100644
--- a/dev/tasks/r/github.macos.brew.yml
+++ b/dev/tasks/r/github.macos.brew.yml
@@ -31,14 +31,17 @@ jobs:
         env:
         {{ macros.github_set_sccache_envvars()|indent(8)}}  
         run: |
+          
           brew install sccache
+          # for testing
+          brew install minio
+          
           # TODO: Update the TODO for ARROW-16907 below to refer to main instead of master
           #       after migrating the default branch to main.
           # TODO(ARROW-16907): apache/arrow@master seems to be installed already
           # so this does nothing on a branch/PR
           brew install -v --HEAD apache-arrow
-          # for testing
-          brew install minio
+
       - uses: r-lib/actions/setup-r@v2
       - name: Install dependencies
         run: |