Christopher Brahney, 22, was last seen at the band's homecoming concert at Heaton Park on Friday (June 29) at around 11.30pm.
The band said in a statement: "If you saw Christopher at the end of the evening please get in touch with Greater Manchester Police and spread the word to everyone who came to the show.
"Our thoughts are with Christopher's family and we all want to see him back at home safe and sound."
Brahney is white, of slim build, and has short brown hair. He was last known to be wearing a dark blue top, light blue shirt, maroon trousers and green wellington boots.
Detectives are investigating the possibility that he boarded a coach at a park-and-ride area in nearby Bowlee Park following reports that he got off a bus there shortly before midnight.
Brahney is thought to have spoken to a group of young women there, telling them how he had lost his phone and his friends, Manchester Evening News reports.
Anyone with information should call the Greater Manchester Police on 0161 856 7652.
Photo gallery - Stone Roses at Heaton Park: