Acting Prime Minister Chester Cooper issued a statement Friday saying that police are investigating and the cause of death was unknown, though foul play "is not suspected."
Their identities were not initially made public.
The health minister, Dr Michael Darville, told Eyewitness News Bahamas on Saturday that some hotel guests went to a clinic Thursday with nausea and vomiting, were treated and left. Three were later found dead. A fourth was flown to a hospital in New Providence.
He said the environmental health scientists, physicians and others were investigating to ensure there was not a public health hazard.
"We feel that what we are seeing is an isolated case associated in a particular area," he said, adding that investigators are doing toxicology and blood tests to help determine the cause of the illness.
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Cooper was filling in for Prime Minister Philip E. Davis, who was out of the country.
The head of communications for the prime minister's office, Latrae L. Rahming, tweeted that the deaths occurred at Sandals Emerald Bay in Exuma.
In a statement to People Magazine, a representative for Sandals confirmed the deaths and said the company was "actively working to support both the investigation as well as the guests' families in every way possible."
There was no immediate further response to an Associated Press inquiry to the hotel company on Saturday.