diff --git a/cpp/src/arrow/compute/CMakeLists.txt b/cpp/src/arrow/compute/CMakeLists.txt
index 1d71c14dca714..1134e0a98ae45 100644
--- a/cpp/src/arrow/compute/CMakeLists.txt
+++ b/cpp/src/arrow/compute/CMakeLists.txt
@@ -19,8 +19,10 @@ add_custom_target(arrow_compute)
 
 arrow_install_all_headers("arrow/compute")
 
-# pkg-config support
-arrow_add_pkg_config("arrow-compute")
+if(ARROW_COMPUTE)
+  # pkg-config support
+  arrow_add_pkg_config("arrow-compute")
+endif()
 
 #
 # Unit tests
diff --git a/cpp/src/arrow/compute/arrow-compute.pc.in b/cpp/src/arrow/compute/arrow-compute.pc.in
index 35bfb51683779..a94a0261cce3b 100644
--- a/cpp/src/arrow/compute/arrow-compute.pc.in
+++ b/cpp/src/arrow/compute/arrow-compute.pc.in
@@ -20,6 +20,6 @@ includedir=@ARROW_PKG_CONFIG_INCLUDEDIR@
 libdir=@ARROW_PKG_CONFIG_LIBDIR@
 
 Name: Apache Arrow Compute
-Description: Compute modules for Apache Arrow
+Description: All compute kernels for Apache Arrow
 Version: @ARROW_VERSION@
 Requires: arrow