Military Pay Protection Act of 2013 - Requires the Secretary of the Treasury, during a government-wide shutdown, to make available to the Secretary of Defense (DOD), and the Secretary of Homeland Security (DHS) in the case of the Coast Guard, out of any amounts in the general fund of the Treasury not otherwise appropriated, such amounts as necessary to continue to provide pay and allowances to members of the Army, Navy, Air Force, Marine Corps, and Coast Guard, including reserve components, who perform active service during the funding gap. Allows for the provision of such pay and allowances, at the discretion of the DOD Secretary, to: (1) DOD civilian personnel providing support to such members, and (2) DOD contractor personnel providing direct support to such members.

Makes additional funding available as necessary to prevent interruptions or delays in the performance of domestic disaster relief and recovery operations.

Defines "government-wide shutdown" as any portion of a fiscal year during which none of the appropriation bills for the fiscal year have become law and an Act or joint resolution making continuing appropriations for the fiscal year is not in effect.