CA chief executive James Sutherland said that advice from the Australian government had identified a potential security risk to Australian interests in Bangladesh.
The team was due to leave Sydney on Monday but will now wait for further security advice before confirming its travel arrangements for the tour.
"We have received advice from DFAT (Department of Foreign Affairs and Trade) and based on that information we are working with security experts and the Bangladesh Cricket Board (BCB) on a revised security plan for the tour," Sutherland said.
"We will wait to receive updated security information early in the week before confirming the team's travel arrangements."
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Later BCB chief executive Nizmuddin Chowdhury appeared taken aback by the news from Sydney.
"We are surprised, because the situation in Bangladesh is very calm and stable," he said.
"Cricket was never interrupted in Bangladesh for security reason and we believe it will never happen.
"We are hopeful the tour will be on schedule, especially for the main matches."