Strong tremors have been felt across the region.
The earthquake was originally reported to have measured 6.8 magnitude.
The tremor cracked walls and a newly-built six-storey building in Imphal collapsed, police said. Other buildings were also reported to have been damaged.
At least five people have been killed in Manipur and more than 30 injured, the Press Trust of India news agency reported.
India`s Meteorological Department said the quake struck at a depth of 17km (about 10 miles).
Panicked residents also fled into the streets in Bangladesh, said the BBC`s Salman Saeed in Dhaka.
At the scene, Paojel Chaoba, Journalist
I was woken up by a terrible jolt and felt my building shake. We ran out into the street below.
It was a complete scene of panic: people were fleeing their homes, and shouting.
Several buildings have collapsed in Imphal, and many others have suffered structural damages.
The worst affected appears to be the Mother`s Market or the `Ima Keithel` area. It is home to lots of buildings, private houses, a hospital and the city`s press club.
Many of them have been damaged in the quake and the entire area has been cordoned off. A number of buildings there have been evacuated.
A number of electricity lines have been damaged and many areas are without power.
At the main regional hospital in Imphal, 37 people have been admitted with injuries.
This, in my experience, is the worst quake to hit Imphal.
Deepak Shijagurumayum, a resident of Imphal, told the AFP news agency by phone that his house was severely damaged by the quake.
"Almost everyone was asleep when it struck and were thrown out of their beds," Mr Shijagurumayum said.
"People were crying and praying in the streets and in open spaces. Hundreds remained outdoors for several hours fearing aftershocks."
Shaking was felt as far away as Kolkata (formerly Calcutta), 600km (370 miles) away. "Many people were seen coming out of their homes in panic," local resident Rabin Dev told AFP news agency.
Indian Prime Minister Narendra Modi tweeted that he had spoken to the region`s chief ministers and federal Home Minister Rajnath Singh "on the situation arising in the wake of the earthquake".
Casualties have not yet been reported on the Myanmar side of the border, which is sparsely populated.
The region has a history of powerful earthquakes caused by the northward collision of the Indian and Eurasian plates. They are moving towards each other at a rate of 4-5cm per year.
In 2005, a magnitude 7.6 quake in Pakistan-administered Kashmir left more than 75,000 people dead.
In April 2015, Nepal suffered its worst earthquake on record with 9,000 people killed and about 900,000 homes damaged or destroyed.
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