The deceased was identified as Enamul Haque, 46, hailing from Goispara village in Panchagarh Sadar upazila. He was the constable of Birganj Police Station in Dinajpur.
Anwar Hossain, superintendent of Dinajpur Police, said that Enamul fell sick 10 days ago. Later, he was diagnosed with coronavirus on June 2.
He was admitted to Birganj Upazila Health Complex on June 3 and referred to Dinajpur M Abdur Rahim Medical College Hospital on June 3.
As his condition deteriorated on Tuesday night, he was being taken to Rajarbagh Police Hospital in the capital but died on the way.
Nineteen members of Bangladesh Police have died of Covid-19 until June 8.
A total of 6,718 policemen were infected with coronavirus across the country while performing duties as of Tuesday.
Bangladesh on Wednesday saw a record growth in the daily COVID-19 cases as the health authorities confirmed the detection of the highest 3,190 new coronavirus patients in the span of 24 hours, raising the total number to 74,865.
During the same period, the death toll rose to 1,012 with the death of 37 more people.
Bangladesh has crossed the 1,000 mark in death toll within 91 days after recording the first death on March 18.