Raspberry Pi is still on Apache 2.2 (2.2.22-13+deb7u4 right now). To use Apache as Proxy for Websockets ("ProxyPass") Apache Module mod_proxy_wstunnel is required.
Apache Module mod_proxy_wstunnel is available in httpd 2.4.5 and later.
How can I add mod_proxy_wstunnel to Apache2 2.2 on Raspberry Pi (Backport mod_proxy_wstunnel)?
Download Apache Source, add patch from Vitkin, compile Apache and add module mod_proxy_wstunnel.so to Apache Modules
Details about the patch: https://gist.github.com/vitkin/6661683
Detailed steps:
# Check apache version (should be 2.2.22 as of writing, if not adjust the next step)
dpkg -s apache2
# Checkout apache source
svn checkout http://svn.apache.org/repos/asf/httpd/httpd/tags/2.2.22/ httpd-2.2.22
# Get patch and apply it
wget https://gist.github.com/vitkin/6661683/raw/873dd8b4de4ad1ff69757ffe48fc574374aedc57/apache-2.2-wstunnel.patch
cd httpd-2.2.22
patch -p1 -i ../apache-2.2-wstunnel.patch
# Build Apache
svn co http://svn.apache.org/repos/asf/apr/apr/branches/1.4.x srclib/apr
svn co http://svn.apache.org/repos/asf/apr/apr-util/branches/1.3.x srclib/apr-util
./buildconf # EDIT: Some commenters noted that buildconf should be run before the configure
./configure --enable-proxy=shared --enable-proxy_wstunnel=shared
make
# Copy the module to apache installation
sudo cp modules/proxy/.libs/mod_proxy_wstunnel.so /usr/lib/apache2/modules
# Create module load file
cd /etc/apache2/mods-available
sudo echo "LoadModule proxy_wstunnel_module /usr/lib/apache2/modules/mod_proxy_wstunnel.so" > proxy_wstunnel.load
# Create symbolic link to load the module
cd /etc/apache2/mods-enabled
sudo ln -s ../mods-available/proxy_wstunnel.load proxy_wstunnel.load
# Add ProxyPass to Site config
cd /etc/apache2/sites-available
# e.g. modify default site config with "sudo nano default"
# and add the following line inside the VirtualHost element:
# "ProxyPass /websockets/mywebsocket ws://mywebsocketserver.com/websockets/mywebsocket"
# Restart Apache
sudo /etc/init.d/apache2 restart