High-Capacity Ammunition Magazine Ban of 2013 - Amends the Brady Handgun Violence Prevention Act to prohibit the importation, sale, manufacture, transfer, or possession, in or affecting interstate or foreign commerce, of a large capacity ammunition feeding device.

Defines a "large capacity ammunition feeding device" to: (1) mean a magazine, belt, drum, feed strip, or similar device that has an overall capacity of, or that can be readily changed to accept, more than 10 rounds of ammunition; and (2) exclude an attached tubular device designed to accept, and capable of operating only with, .22 caliber rimfire ammunition.

Provides exemptions for: (1) devices lawfully possessed before this Act's enactment; (2) federal, state, and local agencies and law enforcement officers; (3) licensees under the Atomic Energy Act for on-site security, off-site training, and transportation of nuclear materials; and (4) authorized testing or experimentation by a licensed firearms manufacturer or importer.

Requires a device manufactured after this Act's enactment to be identified by a serial number and the date it was manufactured conspicuously engraved or cast on the device.

Sets penalties for violations. Subjects devices used or involved in knowing violation of such Act to seizure and forfeiture.

Amends the Omnibus Crime Control and Safe Streets Act of 1968 to authorize the use of Edward Byrne Memorial Justice Assistance Grants for buy-back programs for surrendered large capacity ammunition feeding devices.