The American Band Baroness were on the tour bus which crashed and fell 30ft over a viaduct near Bath.
The incident happened at 11.30am at the junction of Brassknocker Hill and the A36, the fire service said.
A total of nine people were on the coach. Two were trapped and had to be rescued by firefighters.
Seven people have been taken to Royal United Hospital in Bath with what are thought to be relatively minor injuries.
The driver of the coach, who is in his 30s, was taken to Frenchay Hospital in Bristol with life-changing injuries.
The band played at The Fleece in Bristol last night. They were on their way to Southampton when the accident happened.