You can technically ship your monolith application in service fabric. But that will come with some challenges.
In service fabric, Stateful apps is recommended to run at least 3 replicas. So its immune to a node failure. But we can run only one replica of our monolith app. During updates, Services can move from one node to another.
If we have once replica, We will have a downtime which we dont need.
Resource allocation may be a problem if your monolith app needs more resources(cpu and memory) than a single node has. This will become a problem when it moves from one node to another.
If you are fine with the above constraints, Then you can try out the deployment.
Refactoring monolith into smaller apps will be the correct option. But that will take some time.
This document under service fabric discusses about converting a monolith app into microservices.