A man, identified as Pannya Singha Roy, died when a wall collapsed on him while he was working in his garden at Noapara in Ambari area of Jalpaiguri district, District Magistrate Pritha Sarkar said.
Several multi-storeyed buildings developed cracks due to quake in Siliguri in north Bengal, Sub-divisional Officer Dipapriya said.
Incidents of a wall collapse and crack in one house were reported from Telipara in Jalpaiguri district, Sub-divisional Officer Seema Haldar said.
The water of the river Korola, passing through the Jalpaiguri town, rose in waves to a considerable height during the quake, she said.
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The tremor also shook Kolkata where hundreds of people ran out of their homes and offices and assembled on the streets. The tremors were felt in various parts of the city especially in Lake Town, Salt Lake, Dalhousie and Park street areas.
Reports from the districts said it was also experienced in Purulia, Bankura, Burdwan, East Midnapore and Nadia districts.
Chief Minister Mamata Banerjee said that state government was monitoring the situation closely and urged people to stay calm.
"My prayers with the people of Nepal and across India after the massive earthquake. Hope everyone is safe. Stay calm," she tweeted.