The 5.5-magnitude quake struck at 10:38 am (0438 GMT) near the city of Narsingdi, about 33 kilometres (16 miles) from Dhaka, according to the US Geological Survey (USGS).
The Friday morning earthquake sparked terror with many in the Muslim-majority nation of 170 million people at home on their day off.
AFP reporters in Dhaka saw people weeping in the streets while others appeared shocked.
Three people were killed, including a medical student, the health department said.
An eyewitness said masonry from an eight-story building in a Dhaka district had fallen onto a busy road below.
"Many people had gathered at the butcher" when the rubble fell, said Sakib Hossain, 50, who rushed out after hearing a loud bang.
"I saw vans carrying injured people," he added.
The USGS warned of potentially "significant casualties" and damage.
"The government is taking all necessary measures, giving the utmost importance to the safety of the people," interim leader Muhammad Yunus said in a statement.
He said emergency services were "responding swiftly to the reports of damages being received" from across the country, including in Dhaka.
The shaking lasted for 26 seconds with its epicentre in Narsingdi's Madhabdi district, according to the Bangladesh Meteorological Department, which recorded the magnitude as 5.7.
"The situation is being closely monitored, and all relevant departments have been directed to immediately go to the field to assess any possible damages," Yunus said.
Yunus, an 85-year-old Nobel Peace Prize winner, was selected after a mass uprising toppled the government in August 2024 to lead the country to elections slated for February 2026.
Strong tremors were felt as far as the Indian city of Kolkata, more than 325 kilometres away from the epicentre.
AFP reporters there saw people fleeing offices and homes after the sudden jolt.
"I felt tremors and my bed moved... I rushed out of my room," said Sumit Dutta, 66.
There were no immediate reports of casualties or significant damage in India.
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