The affected people, aged between 20 and 35, include two who returned home from Italy recently, IEDCR Director Meerjady Sabrina told reporters.
The other was a family member of one of those two, she said.
"There are in stable condition and are being treated in a hospital," Sabrina said.
Three more people who came in contact with the infected people have been kept in quarantine as a precaution, she added.
Prime Minister Sheikh Hasina said earlier on Sunday her government was prepared to tackle the virus, urging people not to panic.
"Coronavirus has become a global problem. We are monitoring the situation round the clock and taking necessary steps," she said at an event in the capital, Dhaka.
The government on Sunday urged Bangladeshi citizens returning from six countries - China, Italy, South Korea, Singapore, Iran and Thailand - to quarantine themselves in their homes for 14 days.
Authorities in Bangladesh say they have strengthened the screening of travelers and more than 400,000 people have been screened at airports and other border entry points.Experts have warned it may be hard to contain a spread of the illness in densely populated South Asia with its generally poor medical infrastructure.