Fischer, whose career included more than 50 albums, had been stricken two weeks ago and died Thursday at a Burbank hospital.
"Clare Fischer was a major influence on my harmonic concept," jazz veteran Herbie Hancock said in a statement on Fischer's Web site. Hancock credited Fischer's arrangements for the 1950s group the Hi-Lo's with significantly influencing his 1968 record "Speak Like a Child."
The Los Angeles Times said while Fischer, who won two Grammys in the 1980s, was established in the world of jazz, he did not consider himself limited to the genre.
"I relate to everything," he told the newspaper in a 1987 interview. "I'm not just jazz, Latin or classical. I really am a fusion of all of those."
A graduate of Michigan State University, Fischer arranged big-band numbers as a teenager and went on to provide arrangements for George Shearing, Brandy and Carlos Santana. He performed solo and also led the Latin group Salsa Picante.