diff --git a/.github/workflows/r.yml b/.github/workflows/r.yml
index 2a801b6040ec8..3d1f75ede4bb5 100644
--- a/.github/workflows/r.yml
+++ b/.github/workflows/r.yml
@@ -21,24 +21,26 @@ on:
   push:
     paths:
       - ".github/workflows/r.yml"
-      - "ci/scripts/r_*.sh"
-      - "ci/scripts/cpp_*.sh"
-      - "ci/scripts/PKGBUILD"
-      - "ci/etc/rprofile"
       - "ci/docker/**"
+      - "ci/etc/rprofile"
+      - "ci/scripts/PKGBUILD"
+      - "ci/scripts/cpp_*.sh"
+      - "ci/scripts/install_minio.sh"
+      - "ci/scripts/r_*.sh"
       - "cpp/**"
-      - 'docker-compose.yml'
+      - "docker-compose.yml"
       - "r/**"
   pull_request:
     paths:
       - ".github/workflows/r.yml"
-      - "ci/scripts/r_*.sh"
-      - "ci/scripts/cpp_*.sh"
-      - "ci/scripts/PKGBUILD"
-      - "ci/etc/rprofile"
       - "ci/docker/**"
+      - "ci/etc/rprofile"
+      - "ci/scripts/PKGBUILD"
+      - "ci/scripts/cpp_*.sh"
+      - "ci/scripts/install_minio.sh"
+      - "ci/scripts/r_*.sh"
       - "cpp/**"
-      - 'docker-compose.yml'
+      - "docker-compose.yml"
       - "r/**"
 
 concurrency:
@@ -256,6 +258,16 @@ jobs:
         uses: actions/checkout@v4
         with:
           fetch-depth: 0
+      # This must be done before r-lib/actions/setup-r because curl in
+      # Rtools doesn't work on non Rtools' MSYS2 environment. If we
+      # use "shell: bash" after r-lib/actions/setup-r, bash in Rtools
+      # is used on non Rtools' MSYS2 environment.
+      - name: Install MinIO
+        shell: bash
+        run: |
+          mkdir -p "$HOME/.local/bin"
+          ci/scripts/install_minio.sh latest "$HOME/.local"
+          echo "$HOME/.local/bin" >> $GITHUB_PATH
       - run: mkdir r/windows
       - name: Download artifacts
         uses: actions/download-artifact@v3
@@ -282,15 +294,6 @@ jobs:
           working-directory: 'r'
           extra-packages: |
             any::rcmdcheck
-      - name: Install MinIO
-        shell: bash
-        run: |
-          mkdir -p "$HOME/.local/bin"
-          curl \
-            --output "$HOME/.local/bin/minio.exe" \
-            https://dl.min.io/server/minio/release/windows-amd64/archive/minio.RELEASE.2022-05-26T05-48-41Z
-          chmod +x "$HOME/.local/bin/minio.exe"
-          echo "$HOME/.local/bin" >> $GITHUB_PATH
       # TODO(ARROW-17149): figure out why the GCS tests are hanging on Windows
       # - name: Install Google Cloud Storage Testbench
       #   shell: bash
diff --git a/ci/scripts/install_minio.sh b/ci/scripts/install_minio.sh
index 6ea8e1a095c39..e493a183b4543 100755
--- a/ci/scripts/install_minio.sh
+++ b/ci/scripts/install_minio.sh
@@ -17,7 +17,15 @@
 # specific language governing permissions and limitations
 # under the License.
 
-set -e
+set -eu
+
+if [ "$#" -ne 2 ]; then
+  echo "Usage: $0 <version> <prefix>"
+  exit 1
+fi
+
+version=$1
+prefix=$2
 
 declare -A archs
 archs=([x86_64]=amd64
@@ -25,45 +33,60 @@ archs=([x86_64]=amd64
        [aarch64]=arm64
        [s390x]=s390x)
 
-declare -A platforms
-platforms=([Linux]=linux
-           [Darwin]=darwin)
-
 arch=$(uname -m)
-platform=$(uname)
-version=$1
-prefix=$2
-
-if [ "$#" -ne 2 ]; then
-  echo "Usage: $0 <version> <prefix>"
-  exit 1
-elif [ -z ${archs[$arch]} ]; then
+if [ -z ${archs[$arch]} ]; then
   echo "Unsupported architecture: ${arch}"
   exit 0
-elif [ -z ${platforms[$platform]} ]; then
-  echo "Unsupported platform: ${platform}"
-  exit 0
-elif [ "${version}" != "latest" ]; then
+fi
+arch=${archs[$arch]}
+
+platform=$(uname)
+case ${platform} in
+  Linux)
+    platform=linux
+    ;;
+  Darwin)
+    platform=darwin
+    ;;
+  MSYS_NT*|MINGW64_NT*)
+    platform=windows
+    ;;
+  *)
+    echo "Unsupported platform: ${platform}"
+    exit 0
+    ;;
+esac
+
+if [ "${version}" != "latest" ]; then
   echo "Cannot fetch specific versions of minio, only latest is supported."
   exit 1
 fi
 
-arch=${archs[$arch]}
-platform=${platforms[$platform]}
-
 # Use specific versions for minio server and client to avoid CI failures on new releases.
 minio_version="minio.RELEASE.2022-05-26T05-48-41Z"
 mc_version="mc.RELEASE.2022-05-09T04-08-26Z"
 
+download()
+{
+  local output=$1
+  local url=$2
+
+  if type wget > /dev/null 2>&1; then
+    wget -nv --output-document ${output} ${url}
+  else
+    curl --fail --location --output ${output} ${url}
+  fi
+}
+
 if [[ ! -x ${prefix}/bin/minio ]]; then
   url="https://dl.min.io/server/minio/release/${platform}-${arch}/archive/${minio_version}"
   echo "Fetching ${url}..."
-  wget -nv --output-document ${prefix}/bin/minio ${url}
+  download ${prefix}/bin/minio ${url}
   chmod +x ${prefix}/bin/minio
 fi
 if [[ ! -x ${prefix}/bin/mc ]]; then
   url="https://dl.min.io/client/mc/release/${platform}-${arch}/archive/${mc_version}"
   echo "Fetching ${url}..."
-  wget -nv --output-document ${prefix}/bin/mc ${url}
+  download ${prefix}/bin/mc ${url}
   chmod +x ${prefix}/bin/mc
 fi