diff --git a/.ci/test_r_package.sh b/.ci/test_r_package.sh
index e7d36e59ceeb..80ac4f141c2f 100755
--- a/.ci/test_r_package.sh
+++ b/.ci/test_r_package.sh
@@ -20,8 +20,8 @@ if [[ "${R_MAJOR_VERSION}" == "3" ]]; then
     export R_LINUX_VERSION="3.6.3-1bionic"
     export R_APT_REPO="bionic-cran35/"
 elif [[ "${R_MAJOR_VERSION}" == "4" ]]; then
-    export R_MAC_VERSION=4.1.1
-    export R_LINUX_VERSION="4.1.1-1.2004.0"
+    export R_MAC_VERSION=4.1.2
+    export R_LINUX_VERSION="4.1.2-1.2004.0"
     export R_APT_REPO="focal-cran40/"
 else
     echo "Unrecognized R version: ${R_VERSION}"
@@ -81,6 +81,19 @@ if [[ $OS_NAME == "macos" ]]; then
         -pkg $(pwd)/R.pkg \
         -target /
 
+    # Older R versions (<= 4.1.2) on newer macOS (>= 11.0.0) cannot create the necessary symlinks.
+    # See https://github.com/r-lib/actions/issues/412.
+    if [[ $(sw_vers -productVersion | head -c2) -ge "11" ]]; then
+        sudo ln \
+            -sf \
+            /Library/Frameworks/R.framework/Resources/bin/R \
+            /usr/local/bin/R
+        sudo ln \
+            -sf \
+            /Library/Frameworks/R.framework/Resources/bin/Rscript \
+            /usr/local/bin/Rscript
+    fi
+
     # Fix "duplicate libomp versions" issue on Mac
     # by replacing the R libomp.dylib with a symlink to the one installed with brew
     if [[ $COMPILER == "clang" ]]; then
diff --git a/.ci/test_r_package_windows.ps1 b/.ci/test_r_package_windows.ps1
index 62562b471345..ffbfeca897b0 100644
--- a/.ci/test_r_package_windows.ps1
+++ b/.ci/test_r_package_windows.ps1
@@ -78,7 +78,7 @@ if ($env:R_MAJOR_VERSION -eq "3") {
   $env:RTOOLS_BIN = "$RTOOLS_INSTALL_PATH\usr\bin"
   $env:RTOOLS_MINGW_BIN = "$RTOOLS_INSTALL_PATH\mingw64\bin"
   $env:RTOOLS_EXE_FILE = "rtools40v2-x86_64.exe"
-  $env:R_WINDOWS_VERSION = "4.1.1"
+  $env:R_WINDOWS_VERSION = "4.1.2"
 } else {
   Write-Output "[ERROR] Unrecognized R version: $env:R_VERSION"
   Check-Output $false
diff --git a/.github/workflows/r_package.yml b/.github/workflows/r_package.yml
index b2e162610705..8059dbb705a5 100644
--- a/.github/workflows/r_package.yml
+++ b/.github/workflows/r_package.yml
@@ -40,7 +40,7 @@ jobs:
           - os: ubuntu-latest
             task: r-package
             compiler: gcc
-            r_version: 4.0
+            r_version: 4.1
             build_type: cmake
           - os: ubuntu-latest
             task: r-package
@@ -50,27 +50,27 @@ jobs:
           - os: ubuntu-latest
             task: r-package
             compiler: clang
-            r_version: 4.0
+            r_version: 4.1
             build_type: cmake
           - os: macOS-latest
             task: r-package
             compiler: gcc
             r_version: 3.6
             build_type: cmake
-          - os: macOS-latest
+          - os: macOS-10.15
             task: r-package
             compiler: gcc
-            r_version: 4.0
+            r_version: 4.1
             build_type: cmake
           - os: macOS-latest
             task: r-package
             compiler: clang
             r_version: 3.6
             build_type: cmake
-          - os: macOS-latest
+          - os: macOS-10.15
             task: r-package
             compiler: clang
-            r_version: 4.0
+            r_version: 4.1
             build_type: cmake
           - os: windows-latest
             task: r-package
@@ -82,7 +82,7 @@ jobs:
             task: r-package
             compiler: MINGW
             toolchain: MSYS
-            r_version: 4.0
+            r_version: 4.1
             build_type: cmake
           # Visual Studio 2017
           - os: windows-2016
@@ -96,14 +96,14 @@ jobs:
             task: r-package
             compiler: MSVC
             toolchain: MSVC
-            r_version: 4.0
+            r_version: 4.1
             build_type: cmake
           # Visual Studio 2022
           - os: windows-2022
             task: r-package
             compiler: MSVC
             toolchain: MSVC
-            r_version: 4.0
+            r_version: 4.1
             build_type: cmake
           ###############
           # CRAN builds #
@@ -118,17 +118,17 @@ jobs:
             task: r-package
             compiler: MINGW
             toolchain: MSYS
-            r_version: 4.0
+            r_version: 4.1
             build_type: cran
           - os: ubuntu-latest
             task: r-package
             compiler: gcc
-            r_version: 4.0
+            r_version: 4.1
             build_type: cran
-          - os: macOS-latest
+          - os: macOS-10.15
             task: r-package
             compiler: clang
-            r_version: 4.0
+            r_version: 4.1
             build_type: cran
           ################
           # Other checks #
@@ -136,7 +136,7 @@ jobs:
           - os: ubuntu-latest
             task: r-rchk
             compiler: gcc
-            r_version: 4.0
+            r_version: 4.1
             build_type: cran
     steps:
       - name: Prevent conversion of line endings on Windows
@@ -151,13 +151,13 @@ jobs:
       - name: Install pandoc
         uses: r-lib/actions/setup-pandoc@v1
       - name: Setup and run tests on Linux and macOS
-        if: matrix.os == 'macOS-latest' || matrix.os == 'ubuntu-latest'
+        if: startsWith(matrix.os, 'macOS') || matrix.os == 'ubuntu-latest'
         shell: bash
         run: |
           export TASK="${{ matrix.task }}"
           export COMPILER="${{ matrix.compiler }}"
           export GITHUB_ACTIONS="true"
-          if [[ "${{ matrix.os }}" == "macOS-latest" ]]; then
+          if [[ $(echo "${{ matrix.os }}" | head -c5) == "macOS" ]]; then
               export OS_NAME="macos"
           elif [[ "${{ matrix.os }}" == "ubuntu-latest" ]]; then
               export OS_NAME="linux"