Three people have also died in Bangladesh which was jolted by strong tremors; over 40 are injured.
The US Geological Survey said the quake of magnitude 6.7 was 57 kilometres (35 miles) deep and struck 29 kilometres (18 miles) west of Imphal, the capital of Manipur on the border with Myanmar.
The quake struck while many residents were asleep, and roofs and staircases of some buildings collapsed in the city of about 2,70,000 people.
"It was the biggest earthquake we've felt in Imphal," disaster response worker Kanarjit Kangujam told news agency Reuters by telephone.
Disaster rescue workers battled to find workers believed to have been buried beneath the rubble of a building that had been under construction. They were unsure how many might be trapped.
Residents of Imphal said people fled their homes and power and telecoms links were down in the remote region.
Some lashed out at what they called the authorities' slow response, saying that although the Army had begun to clear some debris, it appeared to be short on heavy equipment. "We haven't seen any help from the government side until now," said Kangujam, the disaster response volunteer in Manipur. "The government has not given us any information."
Government officials leading the rescue effort could not immediately be reached for comment.
Prime Minister Narendra Modi tweeted that he was in touch with authorities in the northeast.
Spoke to Rajnath ji, who is in Assam, on the situation arising due to the earthquake & asked him to oversee the situation.- Narendra Modi (@narendramodi) January 4, 2016
Rescue teams from Guwahati, in neighbouring Assam, were scrambling to reach Imphal.