There are several things that may be going on. Your cat may have developed allergies and is pulling out hair because her skin itches. Also, there may be mites present that you cannot see. Your vet can do a skin scraping to see whether mites are present. Also, even though your cat is kept indoors, she may have fleas. Look for little black dots in her fur. This is flea "dirt" (droppings). Finally, this may be due to boredom or anxiety. Have there been any changes in her life or her environment? Does she have plenty of toys? Do you spend at least 15 minutes each day playing with her?
I think the wisest thing for you to do is to take her to the vet so he/she can determine whether there is something going on physically or whether it is a psychological issue.