Officials said 19 other people aboard were examined at a hospital and released after the crash Thursday.
Park spokeswoman Jackie Skaggs said most of the passengers were from China.
No other vehicles were involved in the crash.
Authorities believe the bus went off the pavement and the driver overcorrected, causing the bus to flip on its side and slide, Skaggs said.
The wreck closed the highway, which runs north-south through the park and connects Grand Teton with Yellowstone National Park, for about five hours. Skaggs said the bus was bound for Yellowstone.
The bus driver was among those taken to the hospital in Jackson. It was not immediately known if he had been discharged. His name wasn't released.
Skaggs said no charges had been filed.
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.