diff --git a/ci/docker/python-wheel-manylinux.dockerfile b/ci/docker/python-wheel-manylinux.dockerfile
index 0a50d450c225a..a07c727ac76fa 100644
--- a/ci/docker/python-wheel-manylinux.dockerfile
+++ b/ci/docker/python-wheel-manylinux.dockerfile
@@ -28,7 +28,7 @@ ENV MANYLINUX_VERSION=${manylinux}
 RUN yum install -y dnf
 
 # Install basic dependencies
-RUN dnf install -y git flex curl autoconf zip perl-IPC-Cmd wget kernel-headers
+RUN dnf install -y git flex curl autoconf zip perl-IPC-Cmd wget
 
 # A system Python is required for ninja and vcpkg in this Dockerfile.
 # On manylinux2014 base images, system Python is 2.7.5, while
@@ -97,4 +97,5 @@ SHELL ["/bin/bash", "-i", "-c"]
 ENTRYPOINT ["/bin/bash", "-i", "-c"]
 
 COPY python/requirements-wheel-build.txt /arrow/python/
-RUN pip install -r /arrow/python/requirements-wheel-build.txt
+# TODO(GH-39848) Remove the `--pre --extra-index-url` for numpy nightly again before the 16.0 release 
+RUN pip install -r /arrow/python/requirements-wheel-build.txt --pre --extra-index-url "https://pypi.anaconda.org/scientific-python-nightly-wheels/simple"
diff --git a/ci/docker/python-wheel-windows-vs2017.dockerfile b/ci/docker/python-wheel-windows-vs2017.dockerfile
index faf07800c956a..067105b3a7995 100644
--- a/ci/docker/python-wheel-windows-vs2017.dockerfile
+++ b/ci/docker/python-wheel-windows-vs2017.dockerfile
@@ -88,7 +88,8 @@ RUN choco install -r -y --no-progress python --version=%PYTHON_VERSION%
 RUN python -m pip install -U pip setuptools
 
 COPY python/requirements-wheel-build.txt arrow/python/
-RUN python -m pip install -r arrow/python/requirements-wheel-build.txt
+# TODO(GH-39848) Remove the `--pre --extra-index-url` for numpy nightly again before the 16.0 release 
+RUN python -m pip install -r arrow/python/requirements-wheel-build.txt --pre --extra-index-url "https://pypi.anaconda.org/scientific-python-nightly-wheels/simple"
 
 # ENV CLCACHE_DIR="C:\clcache"
 # ENV CLCACHE_COMPRESS=1
diff --git a/ci/scripts/python_wheel_macos_build.sh b/ci/scripts/python_wheel_macos_build.sh
index fd845c512dcdb..8123a9fdf1c48 100755
--- a/ci/scripts/python_wheel_macos_build.sh
+++ b/ci/scripts/python_wheel_macos_build.sh
@@ -50,12 +50,15 @@ echo "=== (${PYTHON_VERSION}) Install Python build dependencies ==="
 export PIP_SITE_PACKAGES=$(python -c 'import site; print(site.getsitepackages()[0])')
 export PIP_TARGET_PLATFORM="macosx_${MACOSX_DEPLOYMENT_TARGET//./_}_${arch}"
 
+# TODO(GH-39848) Remove the `--pre --extra-index-url` for numpy nightly again before the 16.0 release 
 pip install \
   --upgrade \
   --only-binary=:all: \
   --target $PIP_SITE_PACKAGES \
   --platform $PIP_TARGET_PLATFORM \
-  -r ${source_dir}/python/requirements-wheel-build.txt
+  -r ${source_dir}/python/requirements-wheel-build.txt \
+  --pre \
+  --extra-index-url "https://pypi.anaconda.org/scientific-python-nightly-wheels/simple"
 pip install "delocate>=0.10.3"
 
 echo "=== (${PYTHON_VERSION}) Building Arrow C++ libraries ==="
diff --git a/python/pyproject.toml b/python/pyproject.toml
index 437de105ab8e7..9079618ad1c7d 100644
--- a/python/pyproject.toml
+++ b/python/pyproject.toml
@@ -18,7 +18,12 @@
 [build-system]
 requires = [
     "cython >= 0.29.31",
-    "oldest-supported-numpy>=0.14",
+    # Starting with NumPy 1.25, NumPy is (by default) as far back compatible
+    # as oldest-support-numpy was (customizable with a NPY_TARGET_VERSION
+    # define).  For older Python versions (where NumPy 1.25 is not yet avaiable)
+    # continue using oldest-support-numpy.
+    "oldest-supported-numpy>=0.14; python_version<'3.9'",
+    "numpy>=1.25; python_version>='3.9'",
     "setuptools_scm < 8.0.0",
     "setuptools >= 40.1.0",
     "wheel"
diff --git a/python/requirements-build.txt b/python/requirements-build.txt
index 56e9d479ee9ba..e1372e807f88d 100644
--- a/python/requirements-build.txt
+++ b/python/requirements-build.txt
@@ -1,4 +1,5 @@
 cython>=0.29.31
-oldest-supported-numpy>=0.14
+oldest-supported-numpy>=0.14; python_version<'3.9'
+numpy>=1.25; python_version>='3.9'
 setuptools_scm<8.0.0
 setuptools>=38.6.0
diff --git a/python/requirements-wheel-build.txt b/python/requirements-wheel-build.txt
index f42ee4a018f3c..044f9de5f8214 100644
--- a/python/requirements-wheel-build.txt
+++ b/python/requirements-wheel-build.txt
@@ -1,5 +1,6 @@
 cython>=0.29.31
-oldest-supported-numpy>=0.14
+oldest-supported-numpy>=0.14; python_version<'3.9'
+numpy>=1.25; python_version>='3.9'
 setuptools_scm<8.0.0
 setuptools>=58
 wheel
diff --git a/python/setup.py b/python/setup.py
index d7a2da2077cdd..098d75a3186af 100755
--- a/python/setup.py
+++ b/python/setup.py
@@ -449,7 +449,7 @@ def has_ext_modules(foo):
 
 
 install_requires = (
-    'numpy >= 1.16.6, <2',
+    'numpy >= 1.16.6',
 )