TLF's suggestions are useful delaying tactics but not a full solution. If you are playing long hours without breaks, problems are eventually inevitable.
I think the first thing you have to ask yourself is whether or not you already have a problem and it is just flaring up to a point that you can't bear it when you play Civ for a while. Sounds like that might be the case.
Second thing is to clearly identify all the affected areas. Computer related RSI is normally centred on the tendons and tendon sheaths in the forearm.
1) It sneaks up on you. It takes a while to build up and be just under the radar and then you suddenly really start to feel it and that often means that already have a substantial problem. It is preferable to develop habits that never let it get to that point. Take many breaks, get up, do something else, don't play as long each time, exercise. Look at the ergonomic layout of where you use the computer, i.e. the chair, screen, elevation, type of keyboard and mouse, etc.
2) Solving RSI is more difficult than preventing it. Getting rid of it once and for all is best done through real exercise for the arms, shoulders and back. Something very vigorous like rock climbing if excellent for that as it works the affected muscles and tendons very hard and not only builds them up in a positive way, it puts them into a relaxed state afterwards. Hanging by your arms from a bar is another, simpler way to really stretch out the arms, shoulders, etc. But either way, you have to really work at it to get rid of it for good.
You can also get a small "TENS" unit to massage and relax the affected areas. Those are ok for acute specific problems but RSI normally involves entire systems of muscles and tendons and it is very difficult to involve all of them systemically with a TENS unit.