diff --git a/.env b/.env
index eb87dc62bdd8c..00c238421d301 100644
--- a/.env
+++ b/.env
@@ -49,7 +49,7 @@ ULIMIT_CORE=-1
 ALMALINUX=8
 ALPINE_LINUX=3.16
 DEBIAN=11
-FEDORA=38
+FEDORA=39
 UBUNTU=20.04
 
 # Default versions for various dependencies
diff --git a/ci/docker/fedora-38-cpp.dockerfile b/ci/docker/fedora-39-cpp.dockerfile
similarity index 99%
rename from ci/docker/fedora-38-cpp.dockerfile
rename to ci/docker/fedora-39-cpp.dockerfile
index 2dcc094ee20c5..eb9560dbfbe7e 100644
--- a/ci/docker/fedora-38-cpp.dockerfile
+++ b/ci/docker/fedora-39-cpp.dockerfile
@@ -16,7 +16,7 @@
 # under the License.
 
 ARG arch
-FROM ${arch}/fedora:38
+FROM ${arch}/fedora:39
 ARG arch
 
 # install dependencies
diff --git a/dev/tasks/tasks.yml b/dev/tasks/tasks.yml
index cf04d29715306..8a32724b153fe 100644
--- a/dev/tasks/tasks.yml
+++ b/dev/tasks/tasks.yml
@@ -1104,12 +1104,12 @@ tasks:
       image: debian-cpp
 {% endfor %}
 
-  test-fedora-38-cpp:
+  test-fedora-39-cpp:
     ci: github
     template: docker-tests/github.linux.yml
     params:
       env:
-        FEDORA: 38
+        FEDORA: 39
       image: fedora-cpp
 
 {% for cpp_standard in [20] %}
@@ -1217,12 +1217,12 @@ tasks:
         UBUNTU: 22.04
       image: ubuntu-python
 
-  test-fedora-38-python-3:
+  test-fedora-39-python-3:
     ci: azure
     template: docker-tests/azure.linux.yml
     params:
       env:
-        FEDORA: 38
+        FEDORA: 39
       image: fedora-python
 
   test-r-linux-valgrind:
diff --git a/docker-compose.yml b/docker-compose.yml
index 7ae625a017417..aec685775aab1 100644
--- a/docker-compose.yml
+++ b/docker-compose.yml
@@ -658,7 +658,7 @@ services:
     #   docker-compose run --rm fedora-cpp
     # Parameters:
     #   ARCH: amd64, arm64v8, ...
-    #   FEDORA: 38
+    #   FEDORA: 39
     image: ${REPO}:${ARCH}-fedora-${FEDORA}-cpp
     build:
       context: .
@@ -959,7 +959,7 @@ services:
     #   docker-compose run --rm fedora-python
     # Parameters:
     #   ARCH: amd64, arm64v8, ...
-    #   FEDORA: 38
+    #   FEDORA: 39
     image: ${REPO}:${ARCH}-fedora-${FEDORA}-python-3
     build:
       context: .