Mobile Medical Homeless Health Improvement Act of 2013 - Amends the Public Health Service Act to authorize the Secretary of Health and Human Services (HHS) to award grants, contracts, or cooperative agreements to hospitals or other local health care facilities to improve access of homeless individuals to mobile medical health care services (any health care related services provided in a moveable vehicle or a non-permanents clinic). Directs the Secretary to give priority to applicants from a geographic area that has a comparatively high ratio of homeless individuals to non-homeless individuals. Allows grantees to continue providing services to an individual who has received services under this Act for 12 months after he or she becomes a resident in permanent housing.