diff --git a/python/pyproject.toml b/python/pyproject.toml
index 656d95c6a5897..00437a4f2f8a7 100644
--- a/python/pyproject.toml
+++ b/python/pyproject.toml
@@ -18,11 +18,8 @@
 [build-system]
 requires = [
     "cython >= 0.29",
-    "numpy==1.16.6; python_version<'3.8'",
-    "numpy==1.17.3; python_version=='3.8'",
-    "numpy==1.19.4; python_version=='3.9'",
-    "numpy==1.21.3; python_version>'3.9'",
-    "setuptools < 58.5",  # ARROW-14584
+    "oldest-supported-numpy",
     "setuptools_scm",
+    "setuptools >= 38.6.0",
     "wheel"
 ]
diff --git a/python/requirements-build.txt b/python/requirements-build.txt
index 02539419286ed..09a3060c4dbbb 100644
--- a/python/requirements-build.txt
+++ b/python/requirements-build.txt
@@ -1,4 +1,4 @@
 cython>=0.29
-numpy>=1.16.6
-setuptools>=38.6.0
+oldest-supported-numpy
 setuptools_scm
+setuptools>=38.6.0
diff --git a/python/requirements-wheel-build.txt b/python/requirements-wheel-build.txt
index 5fc0501532109..09abb4b469e82 100644
--- a/python/requirements-wheel-build.txt
+++ b/python/requirements-wheel-build.txt
@@ -1,16 +1,5 @@
 cython>=0.29.11
-setuptools>=58
+oldest-supported-numpy
 setuptools_scm
+setuptools>=58
 wheel
-numpy==1.19.4; platform_system == "Linux"   and platform_machine == "aarch64" and python_version <= "3.9"
-numpy==1.21.3; platform_system == "Linux"   and platform_machine == "aarch64" and python_version >  "3.9"
-numpy==1.16.6; platform_system == "Linux"   and platform_machine != "aarch64" and python_version <  "3.9"
-numpy==1.19.4; platform_system == "Linux"   and platform_machine != "aarch64" and python_version == "3.9"
-numpy==1.21.3; platform_system == "Linux"   and platform_machine != "aarch64" and python_version >  "3.9"
-numpy==1.21.3; platform_system == "Darwin"  and platform_machine == "arm64"
-numpy==1.16.6; platform_system == "Darwin"  and platform_machine != "arm64"   and python_version <  "3.8"
-numpy==1.19.4; platform_system == "Darwin"  and platform_machine != "arm64"   and python_version >= "3.8" and python_version <= "3.9"
-numpy==1.21.3; platform_system == "Darwin"  and platform_machine != "arm64"   and python_version >  "3.9"
-numpy==1.16.6; platform_system == "Windows"                                   and python_version <  "3.9"
-numpy==1.19.4; platform_system == "Windows"                                   and python_version == "3.9"
-numpy==1.21.3; platform_system == "Windows"                                   and python_version >  "3.9"