Military Hunger Prevention Act This bill requires the Department of Defense (DOD) to pay a basic needs allowance to a regular member of the Army, Navy, Marine Corps, or Air Force who is low-income and meets other specified requirements. Specifically, DOD must pay the allowance to such a service member who (1) has completed initial entry training, (2) has a gross household income during the most recent year that does not exceed an amount equal to 130% of the federal poverty guidelines, (3) submits required information to DOD, and (4) does not elect against receiving the allowance for a given year. For purposes of determining eligibility, gross household income does not include any basic allowance for housing received during the year by the service member or by any dependents of the service member in the household. In the event a household contains two or more service members entitled to receive the allowance, only one allowance may be paid in a given year. DOD must annually notify potentially eligible service members and provide them with information on DOD financial management and assistance programs.