Prozac can make you sleepy. According to the National Health Service of the U.K., tiredness is a very common side effect of Prozac, afflicting more than 1 in 10 people who take the drug.
Prozac, more properly known as fluoxetine, is used to treat depression, anxiety, some eating disorders and obsessive-compulsive disorders, according to Net Doctor. The National Health Service describes tiredness as one of the most common side effects of the drug, occurring in more than 10 percent of patients, as do lethargy, insomnia, nausea, diarrhea and feelings of muscle weakness. Less common symptoms include feelings of hot and cold, including cold sweats.