The International Table Tennis Federation (ITTF) is the governing body for all national table tennis associations. As such, the ITTF oversees the rules for the sport. ITTF rules regarding the physical specifications of the ball and the replacement of damaged balls are used by USA Table Tennis.
From the ITTF Laws of Table Tennis:
3.04.02.01.03 If a ball is damaged during a match, it shall be replaced by another of those chosen before the match or, if such a ball is not available, by one taken at random by the umpire from a box of those specified for the competition.
This is in addition to the law that governs the physical specifications of the table tennis ball:
2.03 THE BALL
2.03.01 The ball shall be spherical, with a diameter of 40mm.
2.03.02 The ball shall weigh 2.7g.
2.03.03 The ball shall be made of celluloid or similar plastics material and shall be white or orange, and matt.
International Table Tennis Federation – http://ittf.com/_front_page/ittf.asp?category=General
ITTF Laws of Table Tennis – http://www.paddlepalace.com/Manuals/Rules_ITTF.pdf
Photo – cargocollective.com/rmattgarcia/Ping-Pong-Trophy-1