Military Selective Service Health-Care Personnel Registration Act - Directs the President to have registered with the Selective Service System certain persons who are qualified in health-care occupations that are essential to the armed forces and in which the armed forces are understaffed. Requires all U.S. citizens between the ages of 18 and 46 who are so qualified to register for possible induction. Exempts lawful resident aliens. Outlines certain identifying information which may be required from persons registering under this Act. Provides civil penalties for late registration, and criminal penalties for failure to register. Provides further penalties for any interference with the administration of this Act. Prohibits any regulations prescribed under this Act from taking effect until 30 days after their publication in the Federal Register. Authorizes the Director of Selective Service to waive the publication requirements in the interests of national defense.