diff --git a/cpp/cmake_modules/ThirdpartyToolchain.cmake b/cpp/cmake_modules/ThirdpartyToolchain.cmake
index 01e1ab147af..84d65f59178 100644
--- a/cpp/cmake_modules/ThirdpartyToolchain.cmake
+++ b/cpp/cmake_modules/ThirdpartyToolchain.cmake
@@ -2861,10 +2861,19 @@ function(build_simdjson)
 
   target_compile_definitions(simdjson PUBLIC SIMDJSON_EXCEPTIONS=0)
 
-  # The macOS 11.3 SDK has incomplete C++20 concepts support, which prevents
-  # simdjson headers from compiling. Disable simdjson concepts for this SDK.
-  if(CMAKE_OSX_SYSROOT AND CMAKE_OSX_SYSROOT MATCHES "MacOSX11\\.3\\.sdk$")
-    message(STATUS "Disabling simdjson concepts for macOS SDK 11.3")
+  # macOS SDKs before 13.3 ship a libc++ without <ranges> and with incomplete
+  # <concepts>, but simdjson enables its C++20 concepts API from the compiler's
+  # __cpp_concepts alone, so its headers fail to compile against those SDKs
+  # (GH-55267). Disable simdjson concepts for them. Arrow doesn't use that part
+  # of the simdjson API. simdjson considers these SDKs unsupported and won't fix
+  # this upstream, see https://github.com/simdjson/simdjson/issues/2787.
+  #
+  # The SDK directory name may omit the minor version ("MacOSX11.sdk" on CRAN,
+  # "MacOSX11.3.sdk" in our as-cran CI job), so match both forms. This treats
+  # "MacOSX13.sdk" as too old, which is harmless.
+  if(CMAKE_OSX_SYSROOT AND CMAKE_OSX_SYSROOT MATCHES
+                           "MacOSX(1[0-2](\\.[0-9]+)?|13(\\.[0-2])?)\\.sdk$")
+    message(STATUS "Disabling simdjson concepts for macOS SDK older than 13.3")
     target_compile_definitions(simdjson PUBLIC SIMDJSON_CONCEPT_DISABLED=1)
   endif()