The former Arsenal player tested positive in the routine test carried out on all the players and staff of both Bangladesh and Nepal on Saturday, the day after the hosts' 2-0 win against the visitors.
However, all the other staff and players tested negative.
It is a big blow for the Bangladesh team ahead of their tough World Cup qualifying match against Qatar in Doha on December 4 and the series-decider against Nepal on Tuesday.
As his test report came positive, the British coach went into isolation in his hotel room. It was learned that the 41-year-old has a mild cold and no other serious symptoms.
However, the Bangladesh Football Federation decided to do another test on Sunday to be sure about his condition, said an official.
Assistant coach Stuart Watkiss will run the training sessions of the national team in Jamie's absence.
Also read: Home Minister tests Covid-19 positive