The quake lasted for 15 to 20 seconds and was felt around 10.20 am.
The magnitude of the quake was recorded as 5.5, a report by the Central Seismological Observatory in Shillong said.
The epicentre was two km northwest of Kokrajhar town in Assam and at a depth of 10 km, it said.
People rushed out of their houses and offices in Guwahati and other areas, officials said, adding that there were no reports of loss of life or damage to property.
The tremor was felt in six northern districts of West Bengal as well as the metropolis and its surrounding districts, officials said.
An unconfirmed report said a 22-year-old man, Samrat Das, slipped on a staircase and suffered head injuries while rushing out of a multi-storied building in Siliguri in north Bengal during the quake. He died on his way to a hospital, his mother Usha Das was quoted as saying in the report.
Panic-stricken residents in Patna rushed out of buildings.
The quake was felt in Dumka, Pakur, Sahibganj and Godda districts of Jharkhand.
It was also felt in Shillong and other parts of Meghalaya, but there was no report of any casualty, a police officer said.
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