Just like you can run a .NET Console application in a Docker Container, you can also run a ASP.NET Core application in a Docker Container. I think .NET Core might even be a better candidate for containerization.
Docker is getting very popular. It is also endorsed by Microsoft as the defacto container platform.
Late 2017 I saw a post by Scott Hanselman on running Linux Containers on Windows (LCOW), without using MobyVM (a full, but headless VM in Hyper-V).
Since the release of .NET Core, it is almost a child's play to run .NET on other platform then Windows. With .NET Core one can officially target Windows, Linux and even macOS. But with docker you can run .NET Core on (almost) anything.
The other day I was playing around with .NET Core, I decided to provision a Ubuntu Server Core and play around with .NET Core on Ubuntu.