diff --git a/dev/tasks/python-wheels/osx-build.sh b/dev/tasks/python-wheels/osx-build.sh
index 896bfb2465b..c29fc8eb649 100755
--- a/dev/tasks/python-wheels/osx-build.sh
+++ b/dev/tasks/python-wheels/osx-build.sh
@@ -37,6 +37,9 @@ function build_wheel {
 
     pushd $1
 
+    # For bzip_ep to find the osx SDK headers
+    export SDKROOT="$(xcrun --show-sdk-path)"
+
     # Arrow is 64-bit-only at the moment
     export CFLAGS="-fPIC -arch x86_64 ${CFLAGS//"-arch i386"/}"
     export CXXFLAGS="-fPIC -arch x86_64 ${CXXFLAGS//"-arch i386"} -std=c++11"
diff --git a/dev/tasks/python-wheels/travis.osx.yml b/dev/tasks/python-wheels/travis.osx.yml
index 603614e8a26..dab58d7bce4 100644
--- a/dev/tasks/python-wheels/travis.osx.yml
+++ b/dev/tasks/python-wheels/travis.osx.yml
@@ -15,7 +15,7 @@
 # limitations under the License.
 
 os: osx
-osx_image: xcode11.2
+osx_image: xcode11.3
 language: generic
 
 # don't build twice