diff --git a/cpp/cmake_modules/SetupCxxFlags.cmake b/cpp/cmake_modules/SetupCxxFlags.cmake
index 56dc636b15401..baa168214e4dc 100644
--- a/cpp/cmake_modules/SetupCxxFlags.cmake
+++ b/cpp/cmake_modules/SetupCxxFlags.cmake
@@ -24,7 +24,9 @@ include(CheckCXXSourceCompiles)
 message(STATUS "System processor: ${CMAKE_SYSTEM_PROCESSOR}")
 
 if(NOT DEFINED ARROW_CPU_FLAG)
-  if(CMAKE_SYSTEM_PROCESSOR MATCHES "aarch64|ARM64|arm64")
+  if(CMAKE_SYSTEM_PROCESSOR MATCHES "AMD64|X86|x86|i[3456]86")
+    set(ARROW_CPU_FLAG "x86")
+  elseif(CMAKE_SYSTEM_PROCESSOR MATCHES "aarch64|ARM64|arm64")
     set(ARROW_CPU_FLAG "armv8")
   elseif(CMAKE_SYSTEM_PROCESSOR MATCHES "armv7")
     set(ARROW_CPU_FLAG "armv7")
@@ -33,9 +35,9 @@ if(NOT DEFINED ARROW_CPU_FLAG)
   elseif(CMAKE_SYSTEM_PROCESSOR MATCHES "s390x")
     set(ARROW_CPU_FLAG "s390x")
   elseif(CMAKE_SYSTEM_PROCESSOR MATCHES "riscv64")
-    set(ARROW_CPU_FLAG "riscv")
+    set(ARROW_CPU_FLAG "riscv64")
   else()
-    set(ARROW_CPU_FLAG "x86")
+    message(FATAL_ERROR "Unknown system processor")
   endif()
 endif()