On some reefs, 95% of elkhorn corals have been wiped out by the condition, called white pox.
The finding, published in the journal the Proceedings of the National Academy of Sciences, firmly points to sewage pollution as a potential cause.
It is thought to be the first time that a human gut bacterium has been linked to coral disease.
The problem is particularly bad in the Florida Keys, where human waste is treated in septic fields rather than extensively treated to kill bacteria.
Coral endangered
White pox takes the form of white spots on the coral which spread and kill the coral, destroying the living tissue.
On average, the disease spreads at a rate of 2.5 square centimetres of coral a day.
Researchers from the University of Georgia traced the decline of the elkhorn corals to a particular type of bacteria.
This bacterium, called S. marescens, is often found in the faeces of humans, as well as that of certain animals - and living separately in soil and water.
Professor James Porter, who led the research, said: "Elkhorn used to be the commonest coral in the Caribbean, but now it has been proposed for inclusion on the endangered species list.
"It is the giant redwood of the coral forest."
First find
There is no proof so far that the origin of the disease-causing bacteria is human waste, although the Florida Keys appears to be the worst-affected area.
Professor Porter said: "The implications for people in the Florida Keys are high.
"Everyone down here is in love with the water. They want to do the right thing."
Dr John Bythell, from the Department of Marine Sciences and Coastal Management at Newcastle University, UK, said he thought it was the first time that a bacterium found in humans had been implicated in coral disease.
However, he said that the bacterium might simply be acting opportunistically to attack coral already weakened by other stresses.
These might range from sea temperature changes to overfishing, leading to a build-up of algae, he said.
He said: "We don't know for certain what has really caused this to happen in this part of the Caribbean.
"This is a very marginal habitat, a system very different to the rest of the Caribbean."