Mahmud represented Bangladesh from 1998 to 2006 and played 12 Tests and 77 ODIs.
Mahmud, 49, was the Bangladesh team director on their recent Test tour of Sri Lanka and was supposed to have the same role for the home ODI series that starts on Sunday, against the same opponents. He will also be coaching a team in the Dhaka Premier League which begins May 31.
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Mahmud had reportedly tested negative twice after returning from Sri Lanka but tested positive recently, according to a board official. The Bangladesh squad had started training on May 18, after the Eid break, but Mahmud did not join them.
The BCB currently has a biosecure bubble in place for the ODI series that has hubs in the team hotel and the Shere Bangla National Stadium where all three matches will take place.
Sri Lankan players arrived on May 16 and were in a three-day hard quarantine, while the Bangladesh team that arrived from Sri Lanka also had a three-day home quarantine. Shakib Al Hasan and Mustafizur Rahman were in hotel isolation for 11 days after they returned from the IPL that was suspended earlier this month.
(ESPNCricinfo inputs)