In addition to Soundgarden, Cornell, 52, achieved fame as the frontman for another popular rock band, Audioslave, and was a member of the rock "supergroup" Temple of the Dog.
Variety magazine said Cornell died after appearing late Wednesday at Detroit's Fox Theater, the latest stop on a national tour by Soundgarden.
The Grammy-award winning singer and lyricist was a native of Seattle, Washington.
The cause of Cornell's death was not immediately reported. DM