The other 20 people aboard were taken to a Wyoming hospital for evaluation and treatment and were released after the Thursday crash, park spokeswoman Jackie Skaggs said.
Two of the victims were airlifted to a hospital in Idaho Falls, Idaho, and were listed in fair condition on Friday. Five were hospitalized in Jackson, Wyoming, with non-life-threatening injuries, Skaggs said.
Some of those hospitalized in Jackson might require surgery, she said. No other details were available.
Skaggs said the passengers were from one or more Asian nations, but she didn't have specifics.
The driver was among those taken to the Jackson hospital. It was not immediately known if he had been discharged. His name wasn't released.
The crash occurred on U.S. 89 north of Colter Bay Village on Jackson Lake. Authorities believe the bus went off the pavement and the driver over-corrected, causing the bus to flip on its side and slide, Skaggs said. She didn't know how far it slid.
No other vehicles were involved.
Park rangers and the Wyoming Highway Patrol were investigating. Skaggs said no charges had been filed.
U.S. 89 runs north-south through the park and connects Grand Teton with Yellowstone National Park to the north. It was closed for about four hours after the crash, reopening at 9:20 p.m., Skaggs said.
This is the busiest time of year for Grand Teton and the heavily traveled highway, she said.
Skaggs described the bus as medium sized and said it was bound for Yellowstone.
The driver stayed with the vehicle until all the passengers had been attended to and was taken to the hospital by a park ranger, she said.