No, montelukast should not make you drowsy. Antihistamines are a group of medications that are commonly used to treat allergies and one of the side effects of antihistamines is drowsiness. However, montelukast is not an antihistamine. It is a type of medication known as a leukotriene receptor antagonist. Therefore, montelukast does not typically cause drowsiness as other allergy medications do. That being said, the Prescriber’s Digital Reference (PDR) for montelukast does list fatigue as one of the many possible side effects of taking the medication.