Military Crime Victims' Rights Act of 2013 - Amends the Uniform Code of Military Justice (UCMJ) to provide specific rights for victims of offenses under the UCMJ, including the right to: (1) be protected from the accused; (2) reasonable, accurate, and timely notice of any public proceeding involving the offense; (3) not be excluded from such proceeding (with an exception), and to be heard; (4) confer with trial counsel in the case; (5) full and timely restitution; (6) proceedings free from unreasonable delay; and (7) be treated with fairness and respect for the victim's dignity and privacy.

Requires the military judge to ensure such rights in any court-martial proceeding, and requires all others involved in the matter (counsel, investigators, etc.) to make their best efforts to afford such rights. Provides for the enforcement of such rights throughout the process.

Provides for the assumption of such rights by a legal guardian, family member, or estate representative in the case of a victim who is under 18 years old, incompetent, incapacitated, or deceased.

Directs the Secretary of Defense (DOD) to modify the Manual for Courts-Martial to prescribe regulations for the enforcement of such rights.