The two cricket boards - Cricket Australia (CA) and Bangladesh Cricket Board (BCB) - unanimously took the decision to reschedule the tournament, with the latter confirming the decision in a statement on Thursday afternoon.
"This is understandably disappointing for players and fans of both sides. However, in the current global scenario of the COVID-19 outbreak and considering the nature of the health emergency, the BCB and CA are in agreement that this is the most sensible and practical decision," BCB CEO Nizam Uddin Chowdhury said in a statement.
"We hope that the situation will improve soon and we are able to hold this series at a convenient time in the near future. To that end, the BCB will continue to work closely with CA with whom we share a history of support and cooperation, " he added.
Australia were scheduled to play Tests in Chattogram and Dhaka, starting 11 June, as part of the ICC World Test Championship. However, the global health crisis has forced a rethink.
Commenting on the postponement, Cricket Australia CEO Kevin Roberts said, "Postponing the tour is regrettable.