A man, identified as Pannya Singha Roy, died when a wall collapsed on him when he was working in his garden at Noapara in Ambari area of Jalpaiguri district, District Magistrate Pritha Sarkar said.
At least 66 people were injured in three places of Malda district as portions of the roof collapsed in two school buildings and a bank, police said.
Thirty students were injured at BSB High School at Bhado when the roof collapsed following the quake.
Roof collapse at Naimouja High School at Sujapur left 10 students, including three girls, injured.
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Headmaster of the school, who fell sick after hearing the news, had to be hospitalised along with the students, police said.
Yet another 25 people were injured when portions of a roof collapsed at a nationalised bank branch at Bangitola in Malda district.
Police said the injured included both customers and bank employees.
Cracks developed in several buildings of Siliguri in Darjeeling district, Telipara in Jalpaiguri district and various places of Malda district due to the quake, official sources said.
The area suffered an aftershock around noon, Gopinath Raha, in-charge of Sikkim Meteorological Department said.
The temblor also shook Kolkata where hundreds of people ran out of their homes and offices and assembled on the streets.
It was also experienced in Purulia, Bankura, Burdwan, East Midnapore and Nadia districts, reports from there said.
Chief Minister Mamata Banerjee said the 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.