Brewer, who also won once on the Champions Tour before retiring in 2000, had been battling cancer since October, fiancee Alma Jo McGuire said.
"It was incurable," she said. "It was easier on him and the family that it didn't go any longer than it did."
Brewer won the 1967 Masters for his lone major title a year after he lost an 18-hole playoff to Jack Nicklaus after three-putting the 72nd hole.
"Personally, I could not have been happier for a fellow player when Gay won the Masters in 1967," Nicklaus said. "A year earlier, Gay was playing arguably the most solid golf of anyone at Augusta, and I was fortunate to get into a Monday playoff with him and Tommy Jacobs. Gay had a tough day in the playoff, and although I was delighted to win, I felt badly for him. For Gay to come back the next year and win a green jacket was fitting for such a tremendous person and a darn good player. Around that time, Gay was as good as there was."
Nicklaus first met Brewer during their amateur days.
"What I remember most about Gay is his sense of humor and the kidding he always enjoyed doing," Nicklaus said. "He always had a joke. Gay was just a fun-loving guy and you always looked forward to being around him. One thing you had to do around Gay was to protect your clubs. Gay would walk up to you, look inside your bag, and say, 'Hey, that's a great-looking club. Can I try it?' If he did, there was a good chance he would never return it. Gay must have had the largest collection of borrowed clubs anyone's ever seen. Gay was just a great guy who was great fun to be around."
Brewer made his last appearance in the Masters in 2001.
"We are deeply saddened by the loss of Gay Brewer," said Billy Payne, chairman of the Masters and Augusta National Golf Club. "Gay was a wonderful champion and individual and will be dearly missed in April. We express our heartfelt sympathy to his family."
In June, Picadome Golf Course in Lexington, where Brewer learned to play, changed its name to honor him. Brewer played college golf at the University of Kentucky.