The Los Angeles Times said the New York native was diagnosed with cancer in January and died Sunday. The type of cancer Rose suffered was not reported.
Rose became friends with Woody Allen in a high school art class and helped the Oscar-winning filmmaker pen his early movies "What's Up, Tiger Lily?," "Take the Money and Run" and "Bananas."
He later wrote for the TV comedies "The Smothers Brothers," "All in the Family" and "The Odd Couple," plus "The Tonight Show."
In addition to being his longtime friend and collaborator, Allen also introduced Rose to Judy Wolf, who would become Rose's wife of 40 years, the Times said. She died in 2003.
"Mickey was one of the funniest humans I know, a true original and a total eccentric and a wonderful first baseman," Allen said in a statement this week. "We played a lot of baseball together. Once, when I asked him what death meant to him he said, 'No more malteds.'"
Rose is survived by his daughter Jennifer, a stand-up comedian, son Quincy Rose, a filmmaker, and two grandchildren, the Times said.