3rd iteration on my solution for this, posting here for posterity and to complete this thread.
I’ve made this into a full bash script and will provide a link to a blog post which has a more complete intro and description.
#!/usr/bin/env bash
# Usage:
# timeout 10 docker_iptables.sh
#
# Use the builtin shell timeout utility to prevent infinite loop (see below)
if [ ! -x /usr/bin/docker ]; then
exit
fi
# Create a PRE_DOCKER table
iptables -N PRE_DOCKER
# Default action
iptables -I PRE_DOCKER -j DROP
# Docker Containers Public Admin access (insert your IPs here)
iptables -I PRE_DOCKER -i eth0 -s 192.184.41.144 -j ACCEPT
iptables -I PRE_DOCKER -i eth0 -s 120.29.76.14 -j ACCEPT
# Docker Containers Restricted LAN Access (insert your LAN IP range or multiple IPs here)
iptables -I PRE_DOCKER -i eth1 -s 192.168.1.101 -j ACCEPT
iptables -I PRE_DOCKER -i eth1 -s 192.168.1.102 -j ACCEPT
# Docker internal use
iptables -I PRE_DOCKER -o docker0 -m conntrack --ctstate RELATED,ESTABLISHED -j ACCEPT
iptables -I PRE_DOCKER -i docker0 ! -o docker0 -j ACCEPT
iptables -I PRE_DOCKER -m state --state RELATED -j ACCEPT
iptables -I PRE_DOCKER -i docker0 -o docker0 -j ACCEPT
# Docker container named www-nginx public access policy
WWW_IP_CMD="/usr/bin/docker inspect --format='{{.NetworkSettings.IPAddress}}' www-nginx"
WWW_IP=$($WWW_IP_CMD)
# Double check, wait for docker socket (upstart docker.conf already does this)
while [ ! -e "/var/run/docker.sock" ]; do echo "Waiting for /var/run/docker.sock..."; sleep 1; done
# Wait for docker web server container IP
while [ -z "$WWW_IP" ]; do echo "Waiting for www-nginx IP..."; WWW_IP=$($WWW_IP_CMD); done
# Insert web server container filter rules
iptables -I PRE_DOCKER -i eth0 -p tcp -d $WWW_IP --dport 80 -j ACCEPT
iptables -I PRE_DOCKER -i eth0 -p tcp -d $WWW_IP --dport 443 -j ACCEPT
# Finally insert the PRE_DOCKER table before the DOCKER table in the FORWARD chain.
iptables -I FORWARD -o docker0 -j PRE_DOCKER
Blog post is at http://rudijs.github.io/2015-07/docker-restricting-container-access-with-iptables/