Not limited to Islam, a lot of studies shown that prayer do help in health related conditions of people.

Today, Harvard has produced a research that strengthen this theory. You can read more about it below.

Relaxation-response techniques, such as meditation, yoga, and prayer, could reduce the need for health care services by 43 percent, according to a Harvard-affiliated Massachusetts General Hospital study that looked at participants in a relaxation-response-focused training program.

Source: Relaxation response proves positive | Harvard Gazette