Md Atiar Rahman died while undergoing treatment at Rajarbagh Police Lines Hospital at 10pm on Saturday, the Police Headquarters said in a statement.
He was working as a constable in the control room of Manikganj district police.
Atiar joined the police force on Nov 26, 1984. A native of Faridpur, he is survived by his wife and two daughters.
His body has been sent to his village home where his funeral prayers will be held in the presence of senior local law-enforcement personnel, according to the police.
He will later be buried in his family graveyard.
Bangladesh reported its first cases of COVID-19, the illness caused by the novel coronavirus, on Mar 8. The caseload has since soared to 133,978 while the death toll stands at 1,695.
Almost 10,000 police officers have been infected by the coronavirus so far, according to the Police Headquarters.