When creating a container using the docker run command, the --add-host command can be used to append entries to the /etc/hosts file in the container. In this example, 172.16.0.2 foo.example.com will be appended to /etc/hosts.

sudo docker run --add-host foo.example.com:172.16.0.2 --name my-container my-image:latest

Of if the container already exists the docker update command can be used.

sudo docker update --add-host foo.example.com:172.16.0.2 my-container

You can use the docker inspect command to view the JSON for the container.

~]$ sudo docker inspect my-container | jq .[].HostConfig.ExtraHosts
foo.example.com:172.16.0.2

After the container has been created and is up and running, the docker exec command can be used to examine the /etc/hosts file in the container.

~]# docker exec foo cat /etc/hosts
127.0.0.1   localhost
::1         localhost ip6-localhost ip6-loopback
fe00::0     ip6-localnet
ff00::0     ip6-mcastprefix
ff02::1     ip6-allnodes
ff02::2     ip6-allrouters
172.16.0.2  foo.example.com