Sweating is just one of many side effects associated with Prozac, but it may not always be as harmless as you think. If you notice any sudden changes in your sweat, it’s important to talk with your healthcare provider about what could cause these changes. Sweat is produced by the eccrine glands in the skin, which are responsible for cooling down the body during exercise and regulating water balance. When sweat increases without any physical exertion or changes in water consumption, there may be an underlying health issue at play.