Seven Xbox users burned their hands, while 23 reported smoke damage or damage to their carpets or entertainment centers.
It wasn't immediately clear how long the company had known about the safety issue.
Everywhere except Europe, the recall affects Xboxes manufactured before Oct. 23, 2003. In Europe, it affects those manufactured before Jan. 13, 2004.
Customers can order a free replacement cord by going to the game console's Web site, www.xbox.com. Until a new power cord is delivered, the company is recommending that Xbox users turn off their game players while not in use.