A migraine attack is a moderate or severe headache that usually occurs on one side of the head and is often throbbing or pulsating. The headache is often accompanied by sensitivity to light, sensitivity to sound, nausea, or other symptoms. Menstrual migraine (MM) attacks are migraine attacks that occur in individuals before or during their menstrual period. The main goals of the study are to evaluate the efficacy (how well the medicine works), safety, and tolerability (the degree to which any adverse symptoms can be handled by the patients during the study) of atogepant, compared to placebo (looks like the study treatment but has no medicine in it), for the prevention of MM. Atogepant is an investigational drug being developed for the preventive treatment of menstrual migraine. Participants are randomly assigned to one of the 2 treatment groups called Arms to receive atogepant or matching placebo. There is 1 in a 2 chance for the participant to receive placebo. Approximately 430 adult female participants with menstrual migraine will be enrolled in approximately 85 sites across the world. Participants will receive oral atogepant or matching placebo for 3 menstrual cycles during the double-blind period. During the open-label treatment period, participants will receive atogepant during each menstrual cycle. There may be higher treatment burden for participants in this trial compared to their standard of care. Participants will attend regular visits during the study at a hospital or clinic. The safety and tolerability of the treatment will be checked by medical assessments, blood tests, checking for adverse events and completing questionnaires.