"John Lennon because our world is poorer for the loss of his unique poetic vision to this day," one Twitter user wrote.
The cemetery appreciates the fans of Cornell but has a "strict filming policy."
Jared Leto on the late Linkin Park singer: "That voice will live forever."
Soundgarden's 1994 album is an unflinching, sprawling masterpiece.
Chris Cornell is just the latest grunge frontman to suffer an untimely death.
The singer had performed with his band in Detroit the day of his death, which police are investigating as a suicide.
Soundgarden, which split amicably in 1997, was credited with reinventing heavy metal, inventing grunge, killing heavy metal and killing grunge.