The company said in a statement that it was "shocked" at revelations that he failed a drugs test but was implementing the terms of his deal.
"Even if we presume his innocence until proven otherwise, our contract with Tyson is currently suspended," adidas said.
"adidas has a clear policy on doping and drug use -- each of the agreements with our athletes include a clear clause which states that the agreement shall be terminated by adidas if the athlete is found guilty of the possession or use of drugs or any other prohibited substance by the relevant governing sports body having jurisdiction over the athlete."
Gay, 30, is one of the four fastest men in history and has a personal best of 9.69secs for the 100m and 19.58secs for the 200m.
He was the triple 100m, 200m and 4x100m relay world champion in 2007 and came silver in the half-lap sprint at the 2009 edition but failed to translate that success to Olympic level through bad luck and injury.
On Sunday, he confirmed that he was informed that he had tested positive for a banned stimulant at the US National Trials in June.
He insisted, though, that he had "never knowingly or wilfully taken any supplements or substances that break any rules".
A second high-profile sprinter, Jamaica's Asafa Powell, also confirmed on Sunday that he had failed a drugs test.