The pain could be as a result of strained ligaments or muscles or sudden movement as well. Sprains and strains occur due to many reasons like heavy lifting or sleeping on bad angles in bed. There are other serious causes that can be associated to the pain like a ruptured disk, osteoporosis or skeletal irregularities too. You can get more causes of the pain at, http://www.mayoclinic.com/health/back-pain/DS00171/DSECTION=causes.
I have disc problems in my low back, and the orthopedic doc told me stomach sleeping is one of the worst positions for you back. It's just bad posture and support for the natural shape of your spine. Best is on your side with a pillow between your knees and one under your top arm.