Yes Prozac which is also known by the generic name of fluoxetine has been shown to cause hair loss which is normal.
Usually you'll regrow your hair back once you stop taking the Prozac and if you're losing your hair while taking Prozac and it's not caused by something else then your doctor may advise you to stop taking the Prozac and may prescribe another type of medication.
If you're losing your hair all of a sudden while starting and taking Prozac speak with your doctor because the hair loss can be a result of the Prozac.
I used to be on Prozac myself for awhile and started to lose some hair and then the doctor took me off of the Prozac and put me on some other medication that didn't cause hair loss.
The hair that I lost though did eventually grow back so I wouldn't worry about it too much but do speak with your doctor about the hair loss.