Alves said the body of the former junior welterweight champ was discovered in the morning in the posh seaside resort of Porto de Galinhas, where he arrived on Friday with his wife and 1-year-old son.
Alves said police were investigating. It was unclear how the 37-year-old Canadian died.
A spokeswoman for the public safety department said Gatti's wife and son were unhurt.
"There were no bullet or stab wounds on his body, but police did find blood stains on the floor," the spokeswoman said.
Brazilian boxer and four-time world champion Acelino "Popo" Freitas told the G1 website of Brazil's largest TV network Globo that he was a close friend of Gatti and his wife, and that he "knew they were having some sort of problem and were about to separate."
Known for his straightforward punching and granite-like chin, Gatti captured the junior welterweight title in 1995, when he defeated Tracy Harris Patterson in Atlantic City, N.J. His brawling style and natural charisma made him a fan favorite, and he became one of New Jersey's adopted sons while fighting some of his most memorable battles on the Boardwalk.
"I never saw a crowd show so much love for someone like the way that the crowds flocked to Arturo's fights in Atlantic City," said referee Randy Neumann, who officiated Gatti's last fight against Alfonso Gomez two years ago.
"I mean, they were so into him and the crowds were electric. He just fought his heart out every fight."
Gatti continued to keep a home in New Jersey after he retired in 2007, with a career record of 40-9 and 31 knockouts.
"His entire boxing career he fought with us, we've known him since he was 17," Kathy Duva of promoter Main Events told The Associated Press.
"It's just an unspeakable tragedy. I can't even find words. It's a horror."
Gatti defended his title three times before moving up in weight and getting stopped by Angel Manfredy in 1997. He lost twice more before running off four straight wins, setting up a big payday against Oscar De La Hoya.
Although Gatti was knocked out in the fifth round of a lopsided fight, his almost cult-like following never wavered in its support.
"He just captured the imagination of so many people," Duva said.
"We used to joke it was a crowd like the Grateful Dead's, it was the same people every time."
Gatti would later lose to big names like Floyd Mayweather Jr. and Carlos Baldomir, but it was his three-fight series against Ward that left an indelible impression on fight fans.
The first time they met, in May 2002, the 140-pounders traded devastating blows for 10 rounds before leaving it up to the judges to decide a winner. Ward earned the mixed decision, by one point on one scorecard and two points on another, in what Ring Magazine called "Fight of the Year."
The rematch was just as brutal, with Gatti knocking Ward down in the third round with a big right. Ward not only recovered from the blow, which broke Gatti's hand, but managed to go the distance. This time, Gatti earned a clear unanimous decision.
Gatti and Ward had their rubber match at Boardwalk Hall in June 2003, and it was again called "Fight of the Year" by Ring Magazine. Ward knocked Gatti to the floor in the sixth round, but despite fighting with his right hand broken again, Gatti managed to win the decision.
"I was sitting him at the post-fight press conference - I can't remember which one - and I looked at his hand and it was three times the normal size," Duva said.
"He gave me this goofy grin and he said, 'Yeah, I know. We'll party tonight and I'll go to the hospital tomorrow.'"
Gatti attempted a comeback in July 2007, getting knocked out in seven rounds by Gomez. Afterward, with his legion of fans cheering for him in the arena, Gatti announced his retirement in the dressing room at Boardwalk Hall.
Neumann said it was tough for him to end that fight, simply because of Gatti's incredible ability to come back in fights.
"I couldn't stop that fight, simply because he was Arturo Gatti," Neumann said.
"He was much more dignified to go out that way. He had to be counted out. When he fought, you never knew if he could come back. He looked beaten and still came back."
With that loss, Gatti acknowledged the end of all his travails and triumphs.
"I remember walking away from his last fight, and somebody walked up to him in the casino late at night and congratulated him," Duva said.
"And he said, 'Why did he congratulate me?' And I said, 'He was excited to meet you.' And he kind of looked very surprised by that.
"He had no idea what an icon he was or how much he meant to people."
