diff --git a/cpp/src/arrow/symbols.map b/cpp/src/arrow/symbols.map
index 0149f9515d636..a8825250d0561 100644
--- a/cpp/src/arrow/symbols.map
+++ b/cpp/src/arrow/symbols.map
@@ -18,11 +18,6 @@
 {
   global:
     extern "C++" {
-      # Export pthread_once-related symbols so that two SO files
-      # (e.g. libarrow.so and libplasma.so) don't use separate copies of
-      # those symbols.
-      # See https://github.com/apache/arrow/pull/1953#issuecomment-386057063
-      std::__once*;
       # The leading asterisk is required for symbols such as
       # "typeinfo for arrow::SomeClass".
       # Unfortunately this will also catch template specializations
diff --git a/cpp/src/parquet/CMakeLists.txt b/cpp/src/parquet/CMakeLists.txt
index 3615246ef4c1c..679851020bf07 100644
--- a/cpp/src/parquet/CMakeLists.txt
+++ b/cpp/src/parquet/CMakeLists.txt
@@ -209,8 +209,8 @@ if(NOT APPLE AND NOT MSVC)
   # Localize thirdparty symbols using a linker version script. This hides them
   # from the client application. The OS X linker does not support the
   # version-script option.
-  set(SHARED_LINK_FLAGS
-      "-Wl,--version-script=${CMAKE_CURRENT_SOURCE_DIR}/src/parquet/symbols.map")
+  set(PARQUET_SHARED_LINK_FLAGS
+      "-Wl,--version-script=${CMAKE_CURRENT_SOURCE_DIR}/symbols.map")
 endif()
 
 # Because of PARQUET-1420 (Thrift-generated symbols not exported in DLL),
diff --git a/cpp/src/parquet/symbols.map b/cpp/src/parquet/symbols.map
index e00751e35c320..4bf032dd5846c 100644
--- a/cpp/src/parquet/symbols.map
+++ b/cpp/src/parquet/symbols.map
@@ -21,6 +21,7 @@
   local:
     # devtoolset / static-libstdc++ symbols
     __cxa_*;
+    __once_proxy;
 
     extern "C++" {
       # boost
@@ -34,5 +35,6 @@
       # a system with an older libstdc++ which doesn't include the necessary
       # c++11 symbols.
       std::*;
+      *std::__once_call*;
     };
 };
diff --git a/cpp/src/plasma/CMakeLists.txt b/cpp/src/plasma/CMakeLists.txt
index 729fba7e944a4..fa3b15795ee4a 100644
--- a/cpp/src/plasma/CMakeLists.txt
+++ b/cpp/src/plasma/CMakeLists.txt
@@ -80,6 +80,14 @@ if(ARROW_CUDA)
   add_definitions(-DPLASMA_CUDA)
 endif()
 
+if(NOT APPLE AND NOT MSVC)
+  # Localize thirdparty symbols using a linker version script. This hides them
+  # from the client application. The OS X linker does not support the
+  # version-script option.
+  set(PLASMA_SHARED_LINK_FLAGS
+      "-Wl,--version-script=${CMAKE_CURRENT_SOURCE_DIR}/symbols.map")
+endif()
+
 add_arrow_lib(plasma
               SOURCES
               ${PLASMA_SRCS}
@@ -87,6 +95,8 @@ add_arrow_lib(plasma
               PLASMA_LIBRARIES
               DEPENDENCIES
               gen_plasma_fbs
+              SHARED_LINK_FLAGS
+              ${PLASMA_SHARED_LINK_FLAGS}
               SHARED_LINK_LIBS
               ${PLASMA_LINK_LIBS}
               STATIC_LINK_LIBS
diff --git a/cpp/src/plasma/symbols.map b/cpp/src/plasma/symbols.map
new file mode 100644
index 0000000000000..32c86daa44039
--- /dev/null
+++ b/cpp/src/plasma/symbols.map
@@ -0,0 +1,34 @@
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements.  See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership.  The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License.  You may obtain a copy of the License at
+#
+#   http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied.  See the License for the
+# specific language governing permissions and limitations
+# under the License.
+
+{
+  # Symbols marked as 'local' are not exported by the DSO and thus may not
+  # be used by client applications.
+  local:
+    # devtoolset / static-libstdc++ symbols
+    __cxa_*;
+    __once_proxy;
+
+    extern "C++" {
+      # devtoolset or -static-libstdc++ - the Red Hat devtoolset statically
+      # links c++11 symbols into binaries so that the result may be executed on
+      # a system with an older libstdc++ which doesn't include the necessary
+      # c++11 symbols.
+      std::*;
+      *std::__once_call*;
+    };
+};