Roden said everyone escaped the bus before it went up in flames.
Officers were looking at excessive speed or driver distraction as a possible cause of the crash, he said. Weather didn't appear to be a factor.
The bus was headed eastbound on winding State Route 12 through Red Canyon, a gateway to the national park, when it went off the road around noon.
The injured passengers were taken to Garfield Memorial Hospital, where some were given neck and back braces, said Becki Bronson, a spokeswoman for the Garfield County sheriff's office. Others were given a meal at a nearby Mormon church meeting house.
Sheriff's deputies identified the tour operator as Rein Teen Tours of Wayne, N.J. A woman who answered the phone at Rein Teen Tours said the company would have no comment.