The game retailer — which has more than 6,600 stores around the world — announced the policy with signs placed in its shops, Joystiq reports.
The policy comes as the next generation of console game systems are on the brink of being released. The PlayStation 4 has been the subject of Sony events and many Internet rumors for more than a year. While the company will not confirm any specific release date, most analysts think that it will be sometime in 2013.
Also influencing the decision to stop accepting PS2 trade-ins is the fact that Sony has stopped manufacturing PS2 games and hardware. The final products came out in December 2012. Originally released in October 2000, the 12-year run makes the PS2 the longest-available console game system in history.