Medicare Safe Needle Disposal Coverage Act of 2013 - Amends part D (Voluntary Prescription Drug Benefit Program) of title XVIII (Medicare) of the Social Security Act to cover as a part D drug any devices approved for home use by the Food and Drug Administration (FDA) for the safe and effective containment, removal, decontamination, and disposal of home-generated needles, syringes, and other sharps through a sharps container, decontamination/destructive device, or sharps-by-mail program or similar program.