Turner and his band were not on the bus.
The bus was going eastbound on Highway 46 in San Luis Obispo County, Calif., after a show at the Vina Robles Amphitheatre in Paso Robles.
The crew was traveling to Washington for a concert scheduled for Thursday.
The SLOFD claims that the driver of the bus went off the roadway, plunging the bus into an embankment.
The accident's cause remains unclear.
The casualties, including the person who died, have not yet been identified.
Firefighters said two people from the bus were airlifted to a hospital with major injuries, while five others were hospitalized via ambulance for moderate injuries.
Turner's reps told Fox News in a statement, "Josh Turner and his road family have suffered a devastating loss. Please keep the crew, band and Josh in your thoughts and prayers. All remaining shows in September will be rescheduled for a later date."