diff --git a/.travis/test-wheels.sh b/.travis/test-wheels.sh
index 1b77209c3..1765135ec 100755
--- a/.travis/test-wheels.sh
+++ b/.travis/test-wheels.sh
@@ -56,7 +56,7 @@ if [[ "$platform" == "linux" ]]; then
 
   # Check that the other wheels are present.
   NUMBER_OF_WHEELS=$(ls -1q $ROOT_DIR/../.whl/*.whl | wc -l)
-  if [[ "$NUMBER_OF_WHEELS" != "4" ]]; then
+  if [[ "$NUMBER_OF_WHEELS" != "5" ]]; then
     echo "Wrong number of wheels found."
     ls -l $ROOT_DIR/../.whl/
     exit 1
@@ -67,12 +67,14 @@ elif [[ "$platform" == "macosx" ]]; then
   PY_MMS=("2.7"
           "3.4"
           "3.5"
-          "3.6")
+          "3.6"
+          "3.7")
   # This array is just used to find the right wheel.
   PY_WHEEL_VERSIONS=("27"
                      "34"
                      "35"
-                     "36")
+                     "36"
+                     "37")
 
   for ((i=0; i<${#PY_MMS[@]}; ++i)); do
     PY_MM=${PY_MMS[i]}
diff --git a/python/build-wheel-macos.sh b/python/build-wheel-macos.sh
index 588362e80..30e8b1936 100755
--- a/python/build-wheel-macos.sh
+++ b/python/build-wheel-macos.sh
@@ -16,15 +16,24 @@ DOWNLOAD_DIR=python_downloads
 PY_VERSIONS=("2.7.13"
              "3.4.4"
              "3.5.3"
-             "3.6.1")
+             "3.6.1"
+             "3.7.0")
 PY_INSTS=("python-2.7.13-macosx10.6.pkg"
           "python-3.4.4-macosx10.6.pkg"
           "python-3.5.3-macosx10.6.pkg"
-          "python-3.6.1-macosx10.6.pkg")
+          "python-3.6.1-macosx10.6.pkg"
+          "python-3.7.0-macosx10.6.pkg")
 PY_MMS=("2.7"
         "3.4"
         "3.5"
-        "3.6")
+        "3.6"
+        "3.7")
+# On python 3.7, a newer version of numpy seems to be necessary.
+NUMPY_VERSIONS=("1.10.4"
+                "1.10.4"
+                "1.10.4"
+                "1.10.4"
+                "1.14.5")
 
 mkdir -p $DOWNLOAD_DIR
 mkdir -p .whl
@@ -33,6 +42,7 @@ for ((i=0; i<${#PY_VERSIONS[@]}; ++i)); do
   PY_VERSION=${PY_VERSIONS[i]}
   PY_INST=${PY_INSTS[i]}
   PY_MM=${PY_MMS[i]}
+  NUMPY_VERSION=${NUMPY_VERSIONS[i]}
 
   # The -f flag is passed twice to also run git clean in the arrow subdirectory.
   # The -d flag removes directories. The -x flag ignores the .gitignore file,
@@ -60,7 +70,7 @@ for ((i=0; i<${#PY_VERSIONS[@]}; ++i)); do
     $PIP_CMD install -q setuptools_scm==2.1.0
     # Fix the numpy version because this will be the oldest numpy version we can
     # support.
-    $PIP_CMD install -q numpy==1.10.4 cython==0.27.3
+    $PIP_CMD install -q numpy==$NUMPY_VERSION cython==0.27.3
     # Install wheel to avoid the error "invalid command 'bdist_wheel'".
     $PIP_CMD install -q wheel
     # Add the correct Python to the path and build the wheel. This is only
diff --git a/python/build-wheel-manylinux1.sh b/python/build-wheel-manylinux1.sh
index 8fdee4a1a..db31ff55a 100755
--- a/python/build-wheel-manylinux1.sh
+++ b/python/build-wheel-manylinux1.sh
@@ -13,7 +13,7 @@ rm -f /usr/bin/python2
 ln -s /opt/python/cp27-cp27m/bin/python2 /usr/bin/python2
 
 mkdir .whl
-for PYTHON in cp27-cp27mu cp34-cp34m cp35-cp35m cp36-cp36m; do
+for PYTHON in cp27-cp27mu cp34-cp34m cp35-cp35m cp36-cp36m cp37-cp37m; do
   # The -f flag is passed twice to also run git clean in the arrow subdirectory.
   # The -d flag removes directories. The -x flag ignores the .gitignore file,
   # and the -e flag ensures that we don't remove the .whl directory.