For those looking for a minimal DNS service running on a very small image (~6-7MB)
sudo docker build -t dnsmasq .
sudo mkdir /var/dns
sudo /usr/bin/docker run -d --cap-add=NET_ADMIN -v /var/dns:/etc/dnsmasq.d:rw --name=ns1 dnsmasq
The folder /var/dns contains the zone files which you can so drop in from the docker host. An example file can be found in var/dns/ in this repository.
cp systemd/docker-container@ns1.service to /etc/systemd/system/
systemctl enable docker-container@ns1.service
systemctl start docker-container@ns1.service