How do I make a Minecraft-like dedicated server for my game?

If you useing UE4’s replication system it already have dedicated server support, because what dedicated server is, it’s mode when only server portion is active without client. Dedicated server mode is build in by default here you can find instructions how to do run it:

You can also build engine to have only server, you would need to build it from engine source as server build (or im missed something? ;p). But in usually dedicated server is distributed together with client as buildin feature , at least in Q3 engine times. Minecraft is exception as they developed server and client separately, not long ago they integrated them both.