Can playing indoor field hockey cause a stiff back and how to get rid of it?

Stretching. Yes, playing any sport can cause back tightness. The remedy you should try is stretching. Try to loosen your back with various stretches such as "touching your toes". Remember to stretch before and after activities. Heat may loosen the back muscle and if you have a nice friend or relative who can massage your back that would be great. If the pain persists, see your primary physician.