Christopher Brahney, 22, was last seen at the band's homecoming concert at Heaton Park on Friday (June 29) at around 11.30pm.
A Greater Manchester Police statement said that 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.
Detective Inspector Deborah Oakes said: "Christopher's family are clearly very worried about him and are desperate for any information relating to his whereabouts.
"We would urge anyone who may have seen him to contact the police. Christopher, if you see or hear this appeal, we would ask that you make contact with us or the police as soon as possible."
Anyone with information should call the Greater Manchester Police on 0161 856 7652.
About 225,000 people attended The Stone Roses' three shows at Manchester's Heaton Park over the past weekend.
Photo gallery - Stone Roses at Heaton Park: