She came up with the information at a press briefing at IEDCR.
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The infected patients include two men and one woman, and all of them have been kept in quarantine, said Flora adding that their condition is stable now.
Two of them recently returned home from Italy, she said.
Samples from four people who came in contact with the two infected Italy-returnees were collected for test.
Among them, the woman tested positive for the virus and three other Bangladeshis who came in contact with the infected people have been quarantined, said Flora.
The Italy-returnees contacted the IEDCR over hotline number after seeing the symptoms of virus infection after their return to Bangladesh, she said adding that they were found positive for coronavirus after test.
Flora also said the situation is not like that the virus will spread across the country and schools and colleges have to be shut.
The IEDCR director suggested avoiding unnecessary public gathering to prevent its spread.
She said all the necessary initiatives have been taken to face the situation.
Coronavirus, which was first reported in China’s Wuhan, has infected more than 100,000 people and killed over 3,400.
The virus has emerged in more than 90 countries but more than half of those who contracted the virus have now recovered.
Prime Minister Sheikh Hasina on Sunday urged the people of the country not to be worried regarding coronavirus as Bangladesh has enough capability to face this disease.
"Inshallah, we’ve enough capability (to tackle coronavirus) and we’ll do that. There’s nothing to be worried," she said while inaugurating the function of the International Women’s Day at Osmani Memorial Auditorium.
She said the government is monitoring the situation round the clock and will take immediate appropriate steps if any problem arises in any place.
"All have to remain neat and clean and follow the instructions of the Health Ministry," she said.
Sheikh Hasina said Health Ministry is issuing their instructions daily regarding the corona virus.