The death and injuries were caused by falling debris in and around Imphal, the capital of Manipur state, police said.
The powerful tremor left large cracks in walls and a portion of a popular market building collapsed in the state capital.
A newly constructed six-storey building also collapsed in Imphal, the police control room said.
The early morning tremor was also strongly felt in the Bangladeshi capital Dhaka. Police there said 40 people were being treated at a major hospital, including one university student who jumped from a fourth-floor balcony and was in a critical condition.
India’s meteorological department said the epicenter of the quake was in Tamenglong region of Manipur state, near the country’s borders with Myanmar and Bangladesh.
The US Geological Survey said the depth of the quake was 55km (34 miles).
The tremor hit at 4.35 am (23.05 GMT Sunday) 29km west-northwest of the city of Imphal, USGS said.
People panicked and rushed out of their homes in Gauhati, the capital of neighbouring Assam state, as they felt massive shaking at least twice within 60 seconds.
In its initial assessment, USGS said “some casualties and damage are possible and the impact should be relatively localised”.
It said buildings in the area were largely “highly vulnerable to earthquake shaking”. The area is dotted with small houses and there are few tall buildings in the region.
USGS issued a yellow alert for casualties and damage, with a 35% likelihood of between one and 10 deaths from the tremor.
Residents of Imphal said furniture was knocked over and books fell off shelves. “The ground swayed for almost a minute, jolting people awake in their homes,” said one resident, Apem Arthur.
The tremors were also felt in Kolkata, the capital of West Bengal state, some 600km distant. “Many people were seen coming out of their homes in panic,” said local resident Rabin Dev.
India’s seven northeastern states, joined to the rest of the country by a narrow sliver of land, are located in an area of frequent seismic activity. The border region is remote and sparsely populated on the Myanmar side.