diff --git a/cpp/src/arrow/symbols.map b/cpp/src/arrow/symbols.map
index 49511c6a74934..f216d865001d2 100644
--- a/cpp/src/arrow/symbols.map
+++ b/cpp/src/arrow/symbols.map
@@ -22,11 +22,49 @@
     # devtoolset / static-libstdc++ symbols
     __cxa_*;
 
+
+    # Static libraries that are linked in e.g. the manylinux1 build
+    # Brotli compression library
+    Brotli*;
+    # zlib
+    adler32;
+    adler32_combine;
+    adler32_combine64;
+    crc32;
+    crc32_combine;
+    crc32_combine64;
+    deflate*;
+    inflate*;
+    get_crc_table;
+    zcalloc;
+    zcfree;
+    zError;
+    zlibCompileFlags;
+    zlibVersion;
+    _tr_*;
+    # lz4
+    LZ4_*;
+    # zstandard
+    ZSTD_*;
+    ZSTDv*;
+    HUF_*;
+    HUFv*;
+    FSE_*;
+    FSEv*;
+    ZBUFFv*;
+    ERR_getErrorString;
+    # jemalloc
+    je_arrow_*;
+
     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::*;
+
+      # Statically linked C++ dependencies
+      boost::*;
+      snappy::*;
     };
 };
diff --git a/python/manylinux1/Dockerfile-x86_64 b/python/manylinux1/Dockerfile-x86_64
index 6d72ec7538c0f..69d8d3dbf8cef 100644
--- a/python/manylinux1/Dockerfile-x86_64
+++ b/python/manylinux1/Dockerfile-x86_64
@@ -23,6 +23,9 @@ WORKDIR /arrow/cpp/build-plain
 RUN cmake -GNinja -DCMAKE_BUILD_TYPE=Release -DCMAKE_INSTALL_PREFIX=/arrow-dist -DARROW_BUILD_TESTS=OFF -DARROW_BUILD_SHARED=ON -DARROW_BOOST_USE_SHARED=OFF -DARROW_JEMALLOC=ON -DARROW_RPATH_ORIGIN=ON -DARROW_JEMALLOC_USE_SHARED=OFF ..
 RUN ninja install
 
+ADD scripts/check_arrow_visibility.sh /
+RUN /check_arrow_visibility.sh
+
 WORKDIR /
 RUN git clone https://github.com/apache/parquet-cpp.git
 WORKDIR /parquet-cpp
diff --git a/python/manylinux1/scripts/check_arrow_visibility.sh b/python/manylinux1/scripts/check_arrow_visibility.sh
new file mode 100755
index 0000000000000..27a30f7479bb6
--- /dev/null
+++ b/python/manylinux1/scripts/check_arrow_visibility.sh
@@ -0,0 +1,26 @@
+#!/bin/bash -ex
+# 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.
+
+nm -D -C /arrow-dist/lib64/libarrow.so > nm_arrow.log
+
+if [[ `grep ' T ' nm_arrow.log | grep -v arrow | wc -l` -eq 2 ]]
+then
+    exit 0
+fi
+
+exit 1