Civil Surgeon of the district Dr AHM Anwarul Islam said the policeman, Ramzan, serves as a traffic police in the capital.
Ramzan along with his family came to his village home at Madhugari village on Monday.
On information that they are sick with corona symptoms, a medical team collected samples from the couple and their child.
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After lab tests, Ramzan and his wife found positive for Covid-19, said Dr Anwarul.
Later, the local administration put the house of the policeman under lockdown.
With this, a total of 22 people have so far been infected with coronavirus in the district till Tuesday.
Meanwhile , 11 people have discharged from different hospitals after making recovery from coronavirus in the district.
Some 1,878 policemen tested positive for coronavirus while performing their duties during the pandemic till Tuesday. Among them, 865 are from Dhaka Metropolitan Police (DMP), sources at the Police Headquarters told UNB.
So far, seven policemen died of coronavirus. At present, 4,961 policemen are in quarantine while 1,159 are being treated at isolation units of different hospitals.
Bangladesh has so far reported 250 deaths and 16,660 coronavirus cases till Tuesday.
The country on Tuesday reported 969 of confirmed new coronavirus cases.