Can blood pressure medicine cause your blood pressure to drop to low?

Possibly...: If the blood pressure medicine is at too high a dose or if the person is very sensitive to the medicine, then the blood pressure could drop too low and symptoms could result-like dizziness, passing out, etc. To avoid this, medication is started at a low dose and titrated up slowly. Taking your blood pressure at home is helpful during this process so that you can alert your doctor to low readings.