Like everything with MS, nothing is certain. It could be nerve pain/lesions and it could equally be musculo-skeletal, at least in part. I never had a problem with my back but I do now and it's because the spine has been affected by abnormal gait- plus falls and too much sitting around etc etc. The only thing I can suggest is to go to a physio, who may well be able to help and can at least rule out anything musculo-skeletal in origin.

Like cameron said, sitting around because your not feeling well could definitely do it. I worked in the construction business for years and have had lots of lower back problems in the past. I have now learned what not to do to agitate the problems. If I sleep on my left side my back will hurt when I wake up. Back problems can stem from a lot of things, even stress related muscle stiffness. My back has hurt so bad that I literally could not walk because of the pain and nothing I did would help it, but sometimes I will lean over something I can rest my torso on and let my legs hang with no weight on them for a couple minutes and that would stop the pain for a little while. If you try that and it works it is most likely a spine alignment problem pinching a nerve.