Two among the new cases are overseas returnees and the third patient was infected after coming into contact with another patient, according to the government’s disease control agency.
The government earlier confirmed two deaths from the coronavirus. No deaths have been reported in the last 24 hours.
Of those who were infected five have recovered and returned home.
There have been reports of three deaths of persons showing symptoms of coronavirus infection: one in Sylhet and two others in Khulna. But doctors could not confirm their cases as no tests were carried out.
After cutting air connectivity with 10 countries, including India, on Saturday, Bangladesh barred foreigners from 11 land ports on Sunday.
Bangladesh has barred all public gatherings to stop the spread of the virus while all education, recreation centres and theatres have been shut down. HSC and equivalent exams, too, were suspended on Sunday in an effort to stem the spread of the pandemic.
The global death toll from the virus has hit 13,000 over the last 24 hours while the number of infected rose to above 300,000.
Italy recorded a jump in deaths from coronavirus of almost 800 on Saturday, taking the toll in the world's hardest-hit country to almost 5,000, far surpassing China -- the origin place of the virus -- where the death toll passed 3,200 on Saturday, according to Reuters.