The quake was centered in India's Sikkim state near the border of Nepal.
Reports say several people were injured and some buildings fell in the state's capital of New Delhi. The quake 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.
In neighboring Nepal and Bangladesh, the quake sent people rushing out of their homes, offices and shopping centers.
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, said Sikkim police officials.
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.
The Associated Press contributed to this report.