After reading the docs of Service Fabric and how to run it on Windows Server and on Linux, I cannot find anything talking about how to run it on Nano Server. I think that the game studio named Illyriad are running part of their infrastructure on Azure and Service Fabric on Nano Server. I would like to know if theirs any official support on this matter or if they made it by their own ways? Thanks!
AFAIK there is no support to Nano Server (yet).
Nano server has a very stripped down set of Windows APIs and I believe today SF is using some of those. The same is for .Net Full Framework (which SF depends on!) can't run on Nano Server.
Maybe when SF get support to .Net Core, we will see Nano Server support (since the only .Net version that run on Nano is .Net Core).