Five people died in Nepal, including three crushed when a wall of the British embassy compound collapsed in the capital, Kathmandu.
At least five people died in Sikkim and six elsewhere in India. Several earthquakes have hit the region this year, but none has caused major damage.
The quake struck the mountainous north-eastern Indian state of Sikkim at 18:10 (12:40 GMT), according to the US Geological Survey, and was followed by two strong aftershocks.
Telephone lines were knocked out across the state, while power cuts plunged Gangtok, the capital, into darkness just seconds after the quake hit. TV channels reported buildings buckling and pavements cracking.
They said two major roads had collapsed in the city, which has a population of 50,000. Five people were killed in Sikkim and more than 50 reported injured, according to the state's top official, Chief Secretary Karma Gyatso.
Rescuers were searching for those who may be trapped under fallen buildings in the city, state police chief Jasbir Singh said.
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