Copying my answer from https://stackoverflow.com/a/55704955/5449500
Still there is no official approach to run IE/EDGE inside docker as
"No Windows docker images have GUI, so we cannot test IE11, EDGE."
But,We can install virtual-box and make this happen.
This approach adds extra layer of virtualization[Nesting of virtualization] on the top of docker to make the IE/Edge execution happen and I think in near future it may leads to to performance issue for heavy testing.
If Selenium testing is what you are looking for and don't have heavy load , you can give a try to the approach mentioned in the link.
Youtube - Selenium Windows containers in Docker under Linux
Github - Windows Images
Blogpost - selenium-on-windows-docker-revolution