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 win at the World Championships in 2011, 2013 and 2015.
He ran the first leg for Jamaica’s 4x100m relay team in Beijing, which also included Michael Frater, Asafa Powell and Bolt.
The team won in a then-world record of 37.10 seconds, ahead of Trinidad and Tobago and Japan, who could have their medals upgraded. Brazil would then receive bronze.
Russia’s Tatiana Lebedeva has also been stripped of her Beijing long jump and triple jump silver medals after dehydrochlormethyltestosterone was found in one of her samples.
Carter was tested on the evening of the Beijing final in 2008 but that was found at the time to contain no “adverse analytical finding”.
More than 4,500 tests were carried out at those Games, with nine athletes caught cheating.
An anomaly was discovered in Carter’s submission following the IOC’s decision to retest 454 samples from Beijing using the latest scientific analysis methods.
Carter and the Jamaican National Olympic Committee were told of the adverse finding in May – before the Rio Games – and told his B sample would be tested.
It was reported by Reuters in June that Carter’s A sample had been found to contain methylhexanamine, which has been on the World Anti-Doping Agency (Wada) prohibited list since 2004.
It was reclassified in 2011 as a “specified substance”, meaning one that is more susceptible to a “credible, non-doping explanation”.
Sold as a nasal decongestant in the United States until 1983, methylhexanamine has been used more recently as an ingredient in dietary supplements.
Speaking in June, Bolt said the prospect of having to return the gold was “heartbreaking”.
He told the Jamaica Gleaner: “For years you’ve worked hard to accumulate gold medals and you work hard to be a champion, but it’s one of those things.
“I’m more concerned about the athlete and I hope he gets through it.”