Deaths have been reported from capital Dhaka, Jamalpur, and the northern districts of Rajshahi Lalmonirhat and Panchagarh.
At least 29 others in Dhaka were taken to hospital with injuries sustained during the panic rush.
In Sylhet, which borders northeast India, 32 people injured in similar circumstances were admitted to hospital.
Many of the injured in the capital were students of Dhaka University, said Dhaka Medical College and Hospital police outpost’s Inspector Mozammel Haque.
Many students jumped from the second or third floor of their hostel -- one from as high as the fifth floor rooftop.
As buildings started to shake and sway at 5:05am, thousands jumped out of their beds and desperately tried to get out of their homes.
Atiqur Rahman, 23, died in Dhaka's East Jurain as he tried to rush out of his house after the earthquake struck.
"There seems to be no apparent injury on his body. It is suspected that he suffered a cardiac arrest in panic and died," police Inspector Haque said.
He said Atiqur was a student and used to make money by giving tuition but it was not clear which educational institution he was enrolled in.
Similar deaths were reported from Rajshahi and Lalmonirhat.
A cook at a residential hall at Rajshahi University (RU) died of a cardiac arrest in panic, said Hall Provost Ashraf Uz Zaman.
bdnews24.com’s Lalmonirhat correspondent reported the death of a man at the district’s Patgram,
Local Union Council Member Shah Zamal told bdnews24.com that one panic-stricken Nurul Islam died minutes after rushing out of his home.