Yes, cyclobenzaprine can make you very sleepy and this side effect may get worse with higher doses. Drowsiness is the most commonly reported side effect in studies, occurring in up to 38% (38 out of 100) of people. Fatigue and dizziness may also occur. Avoid or limit the use of alcohol or other sedating medicines while being treated with cyclobenzaprine. Also avoid driving, operating machinery, or other hazardous activities until you know how cyclobenzaprine affects you.