Carter was part of the Jamaican quartet that won the 4x100m in Beijing in 2008.
His was one of 454 selected doping samples retested by the International Olympic Committee (IOC) last year, and has been found to contain the banned stimulant methylhexaneamine.
Bolt, 30, completed an unprecedented ‘triple triple’ in Rio last summer.
He won gold in the 100m, 200m and 4x100m relay to add to his successes in the same events in 2008 and 2012.
Carter, 31, was also part of the squad that won the event in London five years ago and helped Jamaica to win the World Championship in 2011, 2013 and 2015.
Trinidad & Tobago have now been awarded the 2008 relay gold, with Japan upgraded to silver and Brazil given bronze.