The 6.1 magnitude shaking lasted nearly 30 seconds, triggering landslides and damaging numerous buildings near the epicenter, including Buddhist monasteries.
Three of the victims were killed by falling boulders, while eight others died when buildings collapsed.
The sharp quake was also felt widely across Bangladesh and several eastern Indian states.
It also damaged hundreds of houses to the north in neighboring Tibet, according to the Chinese official Xinhua news agency.
Eastern India and Bhutan have experienced catastrophic earthquakes in the past.
A 1897 temblor claimed the lives of more than 1,600 people. That shaking registered an estimated magnitude of 8.7.