diff --git a/dev/tasks/verify-rc/github.linux.amd64.docker.yml b/dev/tasks/verify-rc/github.linux.amd64.docker.yml
index f2c0673314826..97eecd2d28977 100644
--- a/dev/tasks/verify-rc/github.linux.amd64.docker.yml
+++ b/dev/tasks/verify-rc/github.linux.amd64.docker.yml
@@ -41,6 +41,15 @@ jobs:
             {% if distro == 'almalinux' and target|upper == 'PYTHON' %}
             -e ARROW_GANDIVA=OFF \
             {% endif %}
+            {% if distro == "conda" and target == "integration" %}
+            {# JPype doesn't work with Python 3.13.
+             # See also:
+             # * https://discuss.python.org/t/api-for-python-3-13-prevents-use-of-3rd-party-gc-allocators/62709/5
+             # * GH-44386
+             # * GH-44389
+            #}
+            -e PYTHON_VERSION="3.12" \
+            {% endif %}
             -e VERIFY_RC="{{ rc|default("") }}" \
             -e TEST_DEFAULT=0 \
             -e TEST_{{ target|upper }}=1 \
diff --git a/dev/tasks/verify-rc/github.macos.yml b/dev/tasks/verify-rc/github.macos.yml
index 37a3e6f3fd517..e0272e8f4e321 100644
--- a/dev/tasks/verify-rc/github.macos.yml
+++ b/dev/tasks/verify-rc/github.macos.yml
@@ -65,7 +65,6 @@ jobs:
           TEST_DEFAULT: 0
           TEST_{{ target|upper }}: 1
         {% if use_conda %}
-          USE_CONDA: 1
           {% if target == "integration" %}
           # JPype doesn't work with Python 3.13.
           # See also:
@@ -74,6 +73,7 @@ jobs:
           # * GH-44389
           PYTHON_VERSION: "3.12"
           {% endif %}
+          USE_CONDA: 1
         {% endif %}
         run: |
           arrow/dev/release/verify-release-candidate.sh {{ release|default("") }} {{ rc|default("") }}