diff --git a/ci/docker/Dockerfile.build.centos7 b/ci/docker/Dockerfile.build.centos7
index f7b90c9415ec..fab7396dd9aa 100644
--- a/ci/docker/Dockerfile.build.centos7
+++ b/ci/docker/Dockerfile.build.centos7
@@ -88,9 +88,9 @@ SHELL [ "/usr/bin/scl", "enable", "devtoolset-7", "rh-python36", "rh-maven35" ]
 
 # Install minimum required cmake version
 RUN cd /usr/local/src && \
-    wget -nv https://cmake.org/files/v3.13/cmake-3.13.5-Linux-x86_64.sh && \
-    sh cmake-3.13.5-Linux-x86_64.sh --prefix=/usr/local --skip-license && \
-    rm cmake-3.13.5-Linux-x86_64.sh
+    wget -nv https://cmake.org/files/v3.21/cmake-3.21.3-linux-x86_64.sh && \
+    sh cmake-3.21.3-Linux-x86_64.sh --prefix=/usr/local --skip-license && \
+    rm cmake-3.21.3-Linux-x86_64.sh
 
 # ccache 3.7.9 has fixes for caching nvcc outputs
 RUN cd /usr/local/src && \
diff --git a/ci/docker/Dockerfile.build.ubuntu b/ci/docker/Dockerfile.build.ubuntu
index 7077cac976fa..ffa659ab8eb5 100644
--- a/ci/docker/Dockerfile.build.ubuntu
+++ b/ci/docker/Dockerfile.build.ubuntu
@@ -133,7 +133,7 @@ RUN cd /usr/local/src && \
 # Python & cmake
 COPY install/requirements /work/
 RUN python3 -m pip install --upgrade pip && \
-    python3 -m pip install cmake==3.16.6 && \
+    python3 -m pip install cmake==3.21.3 && \
     python3 -m pip install -r /work/requirements
 
 ARG USER_ID=0