However, it was not immediately clear that the deceased person was a member of the missing family, Case said.
The body that was recovered by helicopter was being transported to local authorities for a positive identification.
Meanwhile the search for the missing family which was sailing from Sarasota to Fort Myers continues, he said. The sailboat has not been located but searchers recovered two kayaks that the boat was towing, Case said.
Earlier teams discovered other debris associated with the sailboat, including six life jackets. The sailboat had seven life jackets, which had given authorities and the father's wife and brothers hope of a rescue.
The Coast Guard later tweeted that "personal items" believed to be from the family had been recovered 40 nautical miles off the coast of Sanibel Island.
The kayaks weren't with the life jackets and other debris linked to the sailboat, which also had encouraged searchers but the kayaks were located later Wednesday, Case said.
Discovered debris an ominous sign
The family, which had been living on the 29-foot sailboat in Sarasota for about a year, was sailing to Fort Myers early Sunday when they hit a thunderstorm and rough seas.
The boat, which was equipped with an outboard motor, was "not in the best of shape," and the family was sailing to Fort Myers to work on the sailboat, Case said.
When the storm hit, the father, Ace Kimberly, 45, called his brother and asked him to send some weather reports. Kimberly reported 6-foot seas off the coastline of Englewood, about 30 miles south of Sarasota, a Coast Guard statement said.
"And that's the last they heard of him," Case said.
The brother reported Kimberly and his children -- Roger, 13, Donny, 15, and Becky, 17 -- missing Tuesday. The Coast Guard tracked the voyage, which is about 75 miles via land, and by midmorning Wednesday, an airplane crew discovered a debris field after completing eight search patterns.
It was found about 38 miles off Sanibel Island, a few miles off of Fort Myers' coast.
The debris field included water jugs, a tarp, tennis shoes, a basketball and a propane tank, Case said.
"These items did indeed correlate to his brother's vessel," he said, calling it a "dire finding."
The Coast Guard received no distress call from the vessel, Case said.
He described Kimberly's brothers and wife as frightened but hopeful.
"They are terrified, as you can imagine. They're all feeling what we're all feeling -- anxious, upset and hoping for the best," he said. "We are doing everything we can and throwing everything we can at this search at this time."