They do complement one another but docker has tooling that solves similar problems. Does docker-compose (https://docs.docker.com/compose/) fit your needs?

I use ansible to build a machine from zero software installed on it to running multiple docker containers that also make use of various filesystem stuff on the host, as well as set up other non-docker things on the host like networking, selinux stuff, and crons. I like that ansible is not hardwired towards everything being a container.

I tend to run ansible to setup a VM, e.g. a few packages, lock it down to my taste, and then have ansible run docker-compose to deploy the application(s) of interest.

You wouldn't use docker to manage the host networking (which is where ansible comes in), but packaging whatever is listening on ports as a container works really well for me