The bus was northbound on Highway 93 and nearing the Nevada state line when the driver suffered a physical problem and lost control shortly before 8 p.m., the Arizona highway patrol said.
The vehicle hit a ravine, tore up a small hill, and then bounced and lurched over rough terrain for more than 700 feet before stopping, damaging the front end but remaining upright, patrol spokesman Carrick R. Cook said.
"We believe the driver experienced some sort of the medical condition and he just went off the road," the patrol said in a statement. No other vehicles were involved.
All 48 passengers were injured, but 27 of them were walking wounded with mainly bumps and bruises, Cook said.
"The passengers were pretty much bouncing around," he said.
The six most seriously hurt were flown by helicopter to University Medical Center in Las Vegas, while 15 others with less severe injuries were rushed to area hospitals by road.
UMC spokeswoman Danita Cohen said the six were being treated for nonlife-threatening injuries, such as broken bones and lacerations. She described them as being mostly over 50 years old.
Cook said most of the passengers appeared to be from Asia or Europe, but he didn't have details.
The passengers were returning to Las Vegas following a trip to the Grand Canyon when the crash occurred.
It was the third time in recent years that a tour bus crash in the area claimed lives.
Two years ago, two people were killed and several others injured in a crash on an area highway. In January 2009, seven people died and 10 were injured when a charter bus carrying a group of Chinese tourists on a return trip from the Grand Canyon crashed on U.S. 93, the main highway leading to Hoover Dam.
Four hours after the crash, the bus was sitting upright about 30 feet off the shoulder of the road.
The highway near the crash site was reduced to one lane of traffic for several hours.