The band was also scheduled to headline Friday night at Rock on the Range in Columbus, Ohio. AEG Presents officials say the show will continue on with musical tributes planned to honor Cornell.
"We are devastated to hear about the sudden passing of Chris Cornell last night," reads a message on the landing page of the three-day event.
"He was a true hero to music, the voice of a generation. Our thoughts and prayers are with his family, friends and the entire music community," continues the note, adding that Cornell had "the voice of an angel" and is "now watching down on us as we celebrate and honor him all weekend long."
The Fillmore in Denver, where Soundgarden was scheduled to play May 22, honored the singer with a tribute on their marquee.
In Houston, the Revention Music Center issued a statement reading, "We are greatly saddened to hear of the sudden passing of Chris Cornell. His contribution to music, as well as his kind spirit, will be missed greatly. Our thoughts are with his friends and family at this difficult time."
Soundgarden was set to end their tour at Rocklahoma in Pryor, Oklahoma. On Thursday, organizers took to Facebook to express their condolences.
"We are speechless to hear about the unexpected passing of Chris Cornell last night," the statement reads. "He was a true musical legend that will be missed more than words can express. Our thoughts and prayers go out to his family, friends and the entire rock community."