A video of the 23-year-old's challenge has been shared extensively on social media.
The clip shows other nightclubbers at Vacca Lounge cheering Mejía on as he drinks, while others film him.
Elis Gómez, the owner of the nightclub in the city of La Romana has distanced himself from the event.
The nightclub owner told news agency EFE that Mejía, a regular at the club, took it upon himself to bet a group he could complete the challenge.
Local police have closed Vacca Lounge temporarily so that an investigation can be carried out into Mejía's death.
However no arrests have been made.
The aunt of Mejía, Sandra Perozo, said that his death should serve as an example to young people that "not everyone who says they are a friend is really your friend."
This article originally appeared on the Daily Telegraph.