Enid Knibb said her husband died from liver cancer late Thursday.
He had been receiving treatment in the U.S. but returned to Jamaica this week, she said.
Knibb's manager, Ken Stewart, wrote on Facebook on Wednesday that he was accompanying Knibb on the trip back to the Caribbean island.
"I can only hope we make it back so he can enjoy his family and friends and see his homeland one more time," he wrote.
Knibb was an original member of The Skatalites, a Jamaican ska and reggae band created in 1964. His frenetic style was one of the band's hallmarks and is best heard on songs including "Guns of Navarone" and "Freedom Sounds."
The Skatalites broke up in the 1960s, but reunited two decades later in New York. Two of their albums, Hip Bop Ska and Greetings from Skamania, were nominated for Grammy awards in the 1990s.
Their music has influenced bands including 311, the Mighty Mighty Bosstones and No Doubt.
Knibb last performed with The Skatalites in April.
"Knibb was simply the most important and influential modern drummer this country produced," said Herbie Miller, director of the Jamaica Music Museum. "A master percussionist, he contributed to every style of popular and not so popular musical form...As a drummer he established a rhythmic syntax through bold innovative advances."
Knibb is survived by his wife, five children, seven grandchildren and a great grandchild.