Meyer, who also authored a number of books on musicians, died on Tuesday, his son Cim said, without disclosing the cause of death.
Meyer began his career shortly after World War II, playing with local musicians.
He often has been credited for having been instrumental in making Copenhagen a prominent jazz scene in the 1960s and 1970s, when many American jazz players settled in the Danish capital, which was noted for its relaxed atmosphere and lack of racial tension.
Meyer had his own sextet from 1959 to 1973, and invited Benny Carter, Bill Coleman, Roy Eldridge, Coleman Hawkins and Ben Webster, among others, to play with his band in Copenhagen.
Meyer was active in organizing the Danish jazz federation and associations.
The Politiken newspaper on Friday described Meyer, known for his huge gray beard and wearing red suspenders, as "the giant in Danish jazz."
In recent years, Meyer was best known for creating the International Jazzpar Prize in 1989.
The 200,000 kroner (EUR27,000; US$36,750) award, which was handed out until 2004 when the main sponsor pulled out, has been given to jazz greats such as alto saxophonist Lee Konitz, drummer Roy Haynes, pianist and composer Muhal Richard Abrams and pianist and composer Tommy Flanagan, all Americans, among others.
Meyer is survived by his wife, Karen, and his son, Cim, and daughter, Anne Camilla. His funeral will be held Thursday in Roennede, southern Denmark.