Moscow's warning came after the US shot down a Syrian military plane.
Russia also said it was halting communications with the US aimed at preventing such incidents.
Australia has deployed about 780 military personnel as part of the US-led coalition fighting so-called Islamic State (IS) in both Iraq and Syria.
The halt in operations comes as the coalition and the fighters it is supporting on the ground attempt to oust IS militants from the city of Raqqa, the de facto capital of the "caliphate" they proclaimed in 2014.
"Australian Defence Force protection is regularly reviewed in response to a range of potential threats," the defence department said in a statement.
"ADF personnel are closely monitoring the air situation in Syria and a decision on the resumption of ADF air operations in Syria will be made in due course."
Australia joined the US-led coalition in Syria in September 2015, but did not carry out any operations in the country between March and May this year, according to the defence department.
Its activities in Iraq, where it carried out 80 operations in May alone, will continue.