diff --git a/ci/docker/python-wheel-manylinux.dockerfile b/ci/docker/python-wheel-manylinux.dockerfile
index a9b6b8a855a1e..452809ad09c6b 100644
--- a/ci/docker/python-wheel-manylinux.dockerfile
+++ b/ci/docker/python-wheel-manylinux.dockerfile
@@ -114,8 +114,10 @@ RUN PYTHON_ROOT=$(find /opt/python -name cp${PYTHON_VERSION/./}-${PYTHON_ABI_TAG
 SHELL ["/bin/bash", "-i", "-c"]
 ENTRYPOINT ["/bin/bash", "-i", "-c"]
 
-COPY python/requirements-wheel-build.txt /arrow/python/
+# Remove once there are released Cython wheels for 3.13 free-threaded available
 RUN if [ "${python_abi_tag}" = "cp313t" ]; then \
       pip install cython --pre --extra-index-url "https://pypi.anaconda.org/scientific-python-nightly-wheels/simple" --prefer-binary ; \
     fi
+
+COPY python/requirements-wheel-build.txt /arrow/python/
 RUN pip install -r /arrow/python/requirements-wheel-build.txt
diff --git a/ci/scripts/python_wheel_macos_build.sh b/ci/scripts/python_wheel_macos_build.sh
index df99f59ad0945..3fcf8a0301aa9 100755
--- a/ci/scripts/python_wheel_macos_build.sh
+++ b/ci/scripts/python_wheel_macos_build.sh
@@ -49,6 +49,7 @@ fi
 echo "=== (${PYTHON_VERSION}) Install Python build dependencies ==="
 export PIP_SITE_PACKAGES=$(python -c 'import site; print(site.getsitepackages()[0])')
 
+# Remove once there are released Cython wheels for 3.13 free-threaded available
 FREE_THREADED_BUILD="$(python -c"import sysconfig; print(bool(sysconfig.get_config_var('Py_GIL_DISABLED')))")"
 if [[ $FREE_THREADED_BUILD == "True"  ]]; then
   pip install cython --pre --extra-index-url "https://pypi.anaconda.org/scientific-python-nightly-wheels/simple" --prefer-binary