"We were terribly shocked," Blue Jays president Paul Godfrey told The Associated Press. "From what we understand he was in Brandon ... to be the best man at a wedding today."
Godfrey didn't have particulars on the cause of death.
"Obviously, when a 28-year-old man dies, ballplayer or not, it's a terrible, terrible thing," he said.
Kennedy spent seven years in the majors, playing last season with Oakland, Arizona and Toronto. He also spent time with Tampa Bay and Colorado and had a 43-61 career record with a 4.79 ERA in 222 appearances.
"He was such a focused kid from the time we took him in the draft," said Florida Marlins vice president Dan Jennings, who was the scouting director for Tampa Bay when the Rays selected Kennedy in the 1998 draft. "He was on a mission to become a major league pitcher."
Kennedy made his major league debut in June 2001 and made his last appearance in relief on Sept. 29 in a 5-3 win over Tampa Bay.
"You think all athletes and all young people are invincible," Jennings said. "Then when you see something like this, it's very tragic."
Craig Weissmann, the Tampa Bay scout who signed Kennedy, described him as a fierce, determined competitor.
"He really dedicated himself and was really on a mission to become a major league pitcher," Weissmann said. "You wish as a scout and a major league organization, you wish every kid could develop that fast."
Godfrey said Toronto was interested in bringing Kennedy back.
"We had every intention to speak to him," he said. "We had him on our list to talk to."
Kennedy's agent, Damon Lapa, did not return phone calls and an e-mail from the AP.
"He was a valued teammate and friend to everyone with the A's organization," Oakland assistant general manager David Forst said in a statement. "On behalf of the entire A's organization, we extend our condolences to Joe's wife, Jami and his entire family."