Among the new cases, a 70-year-old patient is in a critical condition, Prof Nasima Sultana, additional director general of Directorate General of Health Services, said at a media briefing in Dhaka on Friday.
No death from the coronavirus has been reported in the last 24 hours, she said.
Bangladesh had earlier reported one death from the coronavirus.
One of the new patients is a woman, aged over 30. The other two are men with one aged more than 30.
The septuagenarian is in intensive care for comorbidity or other health complications, said Nasima Sultana.
The man in his 30s retuned to Bangladesh from Italy while the other two patients got infected after they came into contact with the others. The woman came into contact with an Italy returnee.