The bus carrying 50 people, mostly tourists, fell off an around 10-metre-high cliff after crashing into a sports utility vehicle and a pick-up truck around 4.25 p.m. Saturday on a national highway in the county, Xinhua reported.
The bus passengers were mainly tourists from Anhui, Shanghai, Shandong and Hebei regions.
At the time of the accident, four people were in the sports utility vehicle and one was in the truck.
The injured were being treated at several hospitals in Lhasa and their injuries were not life-threatening.
An investigation into the cause of the accident was under way.
Police have detained managers of the Feixiang Travel Agency and the Shengdi Vehicle Tour Company in connection with the accident.