The quake, with a preliminary magnitude of 6.9, was felt across northeast India including the capital of New Delhi. It triggered at least two aftershocks of magnitude 6.1 and 5.3, Indian seismology official R.S. Dattatreyan said. He warned more aftershocks were possible.
At least four people in India's Sikkim state were killed and an unspecified number of people were injured, state police Chief Jasbir Singh told The Associated Press. Nepal's government said five people died and dozens were hurt there.
The full extent of damage was not immediately known because the region is sparsely populated with many living in remote areas which were cut off by mudslides triggered by the quake, Singh said.
TV stations reported buildings collapsed and sidewalks cracked in Sikkim's state capital of Gangtok, 42 miles (68 kilometers) southeast of the quake's epicenter. The Indo-Tibetan Border Police said two of its buildings had collapsed in Gangtok.
Rescuers were working overnight to search for anyone pinned under fallen buildings in the city, which has a population of 50,000, Singh said.
"We have sounded a high alert. Police are on the streets in Gangtok and other major towns," he said.
Electricity and some phone service was interrupted in the area.
Power lines snapped in the West Bengal cities of Darjeeling and Kalimpong, which "are now in total darkness," state Chief Minister Mamata Banerjee said.
Prime Minister Manmohan Singh offered to send troops to help, and summoned the National Disaster Management Authority for an emergency meeting. The air force sent five planes to help with rescue efforts.
In neighboring Nepal and Bangladesh, the quake sent residents rushing out of their homes, offices and shopping centers.
In Nepal's capital of Katmandu, members of parliament who were debating the national budget ran out of the assembly hall into a parking area. They returned 15 minutes later and resumed their session.
The quake was also felt as far as the Indian capital, with New Delhi residents also rushing out of shaking buildings.
Associated Press writers Binaj Gurubacharya in Katmandu, Nepal, and Julhas Alam in Dhaka, Bangladesh, contributed to this report.