Australian foreign office said in a statement that Canberra also authorised the dependants of posted Australian staff to return to the country on a voluntary basis.
"The Australian Government has authorised the dependants of posted Australian staff to return to Australia on a voluntary basis, and will withdraw Australian Government funded volunteers by 31 December," the statement said.
"We advise you (Australians) to exercise a high degree of caution in Bangladesh due to the high threat of terrorist attack and the uncertain political situation," the statement said, adding that Canberra's previously issued level of advice or travel alert regarding Bangladesh remained unchanged.
The directive came hours after US-based jihadist monitor SITE Intelligence group posted a statement that Islamic State (IS) claimed credit for the November 26 attack on a Shia mosque in Bangladesh's Bogra district that killed one person and left three others wounded.
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Bangladesh has repeatedly rejected claims of active presence of international Islamist outfits such as IS and al Qaeda in the country.
But the Australian foreign office said since September a number of attacks claimed by the IS have occurred in Bangladesh, some targeting foreigners.
"As a result of the terrorism threat, Australian officials in Bangladesh have been advised to avoid travel at night, and limit their movements in public places, including bars, hotels and events and locations frequented by foreigners," it said.
Bangladesh witnessed killings of two foreigners, two policemen, a publisher and the fatal attack on a Shia rally, all in the past three months sparking international uproar.