The reason for Kravitz's departure was not reported.
Irish actor Brendan Gleeson will play music promoter Freddy Cousaert in the film, which is to start shooting this month, the entertainment industry trade newspaper said.
The movie will follow Gaye's attempt to get his career back on track after it was derailed by his battles with depression and an addiction to drugs.
The famous singer-songwriter was shot and killed by his father during an argument when he was high on drugs in 1984. He was 44.
In addition to his stint on ""Law & Order," Martin also was an original cast member in the New York stage production and subsequent movie musical adaptation of "Rent." He can now be seen on TV's "Smash."