Lynch is the second Irish rider to be suspended in two Olympic Games
Four horses involved in the Olympic show jumping have tested positive for the banned substance capsaicin.
As a result, they were thrown out of Thursday's individual show jumping final in Beijing, eventually won by Canada's Eric Lamaze on Hickstead.
Ireland's Denis Lynch, riding Lantinus, was among the riders barred.
Norway's Tony Andre Hansen on Camiro, Brazil's Bernardo Alves on Chupa Chup and Germany's Christian Ahlmann on Coster were also ejected.
Lynch, Hansen and Alves had all been scheduled to compete in Thursday's individual competition, but Ahlmann was not entered into the event.
Following news of Lantinus' positive drugs test, Horse Sport Ireland said that Lynch had admitted using a product called Equi-block, which contains capsaicin, on his horse.
Capsaicin, derived from chilli peppers, can have hypersensitising effects or act as a pain relief that, in both cases, can improve the performance of the horse.
It has always been an illegal substance but the technique to discover its use has only recently been developed.
"Denis Lynch explained to the tribunal that he commonly applies Equi-block to the horse's lower back prior to exercise," said a Horse Sport Ireland spokesman.
The Irish official added that a urine sample from the horse had been submitted to a voluntary screening testing on the horse's arrival in Hong Kong and the results of this test were negative.
Lynch was competing as an individual because Ireland did not qualify for the team competition.
He described himself as shattered after being denied the opportunity to compete for an Olympic medal, adding "we have nothing to hide and have done nothing wrong".
If the horses' B sample tests confirm their A samples, their countries will be disqualified from the team show jumping, which took place on Monday.
The announcement throws into doubt the medal order of that competition.
Norway won a bronze medal, its first ever placing in an Olympics equestrian event, while the United States took gold and Canada silver.
Capsaicin is basically rubbed onto the front of the legs and it makes the horses pick up their legs
BBC equestrian commentator Michael Tucker
Norway's bronze is now in jeopardy, with that medal potentially heading Switzerland's way.
In its statement, the International Equestrian Federation (FEI) said the four horses had been "provisionally suspended by the FEI further to doping/medication control tests that indicated the present of capsaicin in each horse".
"Capsaicin is classified as a 'doping' prohibited substance given its hypersensitising properties, and as a 'medication class A' prohibited substance for its pain relieving properties."
The development casts another shadow over the equestrian after positive drugs tests forced a medal re-allocation at the 2004 Athens Games.
Germany were stripped of the team jumping gold in Athens after the horse ridden by Ludger Beerbaum, who is a lynchpin of his country's team in Beijing, was disqualified for a positive test.
Also in Athens, the Irishman Cian O'Connor was stripped of his individual gold medal on Waterford Crystal.
BBC equestrian commentator Michael Tucker told BBC Radio 5 Live: "It's very bad news all round, particularly as two of them were highly thought of as individual medals and all four riders are world-class jockeys.
"Capsaicin is basically rubbed onto the front of the legs and it makes the horses pick up their legs.
"The testing facilities and laboratories here in Hong Kong are second to none in the world class. The B samples are going to be carried out very, very quickly indeed.
"Norway will drop out of the medals and Switzerland will come up."