Background Though associations between obstructive sleep apnea (OSA) and cardiovascular outcomes are well described, limited data exist regarding the impact of OSA on sex‐specific outcomes after acute myocardial infarction (AMI). Methods and Results The VIRGO (Variation in Recovery: Role of Gender on Outcomes of Young AMI Patients) study enrolled 3572 adults aged 18 to 55 years with AMI from the United States and Spain during 2008 to 2012. We included patients for whom the Berlin Questionnaire for OSA was scored at the time of AMI admission (3141; 2105 women, 1036 men). We examined the sex‐specific association between baseline OSA risk with functional outcomes including health status and depressive symptoms at 1 and 12 months after AMI. Among both groups, 49% of patients were at high risk for OSA (1040 women; 509 men), but only 4.7% (148) of patients had a diagnosed history of OSA. Though patients with a high OSA risk reported worse physical and mental health status and depression than low‐risk patients in both sexes, the difference in these functional outcomes was wider in women than men. Moreover, women with a high OSA risk had worse health status, depression, and quality of life than high‐risk men, both at baseline and at 1 and 12 months after AMI. Conclusions Young women with a high OSA risk have poorer health status and more depressive symptoms than men at the time of AMI, which may place them at higher risk of poorer health outcomes over the year following the AMI. Further, the majority of patients at high risk of OSA are undiagnosed at the time of presentation of AMI.