I have .NET Core Azure Service Fabric application and I want to deploy it to my Ubuntu Linux server.
There is tutorial for Windows Server Deployment https://learn.microsoft.com/en-us/azure/service-fabric/service-fabric-cluster-creation-for-windows-server
There is also tutorial for Azure Linux deployment
Is it possible to run ASF on-premise on Linux?
Nope, see the docs:
Standalone clusters currently aren't supported for Linux. Linux is supported on one-box for development and Azure Linux multi-machine clusters.
and
Supported operating systems for standalone clusters
You are able to create clusters on VMs or computers running these operating systems (Linux is not yet supported):
Windows Server 2012 R2
Windows Server 2016