diff --git a/ci/docker/ubuntu-22.04-cpp.dockerfile b/ci/docker/ubuntu-22.04-cpp.dockerfile
index 88a27efe335..3065b0f3dae 100644
--- a/ci/docker/ubuntu-22.04-cpp.dockerfile
+++ b/ci/docker/ubuntu-22.04-cpp.dockerfile
@@ -23,6 +23,17 @@ SHELL ["/bin/bash", "-o", "pipefail", "-c"]
 RUN echo "debconf debconf/frontend select Noninteractive" | \
         debconf-set-selections
 
+# Install CUDA 13 compatibility layer for systems with CUDA 12 drivers
+# This is required for runs-on GPU instances which have CUDA 12.9 drivers
+# See: https://docs.nvidia.com/deploy/cuda-compatibility/forward-compatibility.html
+ARG cuda
+RUN if [ -n "${cuda}" ] && [ "$(echo ${cuda} | cut -d. -f1)" = "13" ]; then \
+      apt-get update -y -q && \
+      apt-get install -y -q --no-install-recommends cuda-compat-13-0 && \
+      apt-get clean && \
+      rm -rf /var/lib/apt/lists*; \
+    fi
+
 # Installs LLVM toolchain, for Gandiva and testing other compilers
 #
 # Note that this is installed before the base packages to improve iteration
diff --git a/ci/docker/ubuntu-24.04-cpp.dockerfile b/ci/docker/ubuntu-24.04-cpp.dockerfile
index 0347d452d7b..fafc4fcea41 100644
--- a/ci/docker/ubuntu-24.04-cpp.dockerfile
+++ b/ci/docker/ubuntu-24.04-cpp.dockerfile
@@ -23,6 +23,17 @@ SHELL ["/bin/bash", "-o", "pipefail", "-c"]
 RUN echo "debconf debconf/frontend select Noninteractive" | \
         debconf-set-selections
 
+# Install CUDA 13 compatibility layer for systems with CUDA 12 drivers
+# This is required for runs-on GPU instances which have CUDA 12.9 drivers
+# See: https://docs.nvidia.com/deploy/cuda-compatibility/forward-compatibility.html
+ARG cuda
+RUN if [ -n "${cuda}" ] && [ "$(echo ${cuda} | cut -d. -f1)" = "13" ]; then \
+      apt-get update -y -q && \
+      apt-get install -y -q --no-install-recommends cuda-compat-13-0 && \
+      apt-get clean && \
+      rm -rf /var/lib/apt/lists*; \
+    fi
+
 # Installs LLVM toolchain, for Gandiva and testing other compilers
 #
 # Note that this is installed before the base packages to improve iteration
diff --git a/compose.yaml b/compose.yaml
index 84481e1af76..f370f430ff7 100644
--- a/compose.yaml
+++ b/compose.yaml
@@ -555,6 +555,7 @@ services:
         base: nvidia/cuda:${CUDA}-devel-ubuntu${UBUNTU}
         clang_tools: ${CLANG_TOOLS}
         cmake: ${CMAKE}
+        cuda: ${CUDA}
         llvm: ${LLVM}
     shm_size: *shm-size
     ulimits: *ulimits