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Michael O'Neill, 47, was killed on Wednesday, leaving behind three children as well as five siblings.
"This is a tragedy and I want to give my condolences to the family of the man involved," Anthony Albanese said in Sydney on Saturday.
"The family has requested that their privacy be respected and I ask the media to do that."
In a public post on Facebook, one of Mr O'Neill's sisters said he had been driving trucks in Ukraine to help civilians flee the country as well as helping transport the wounded.
She described her brother as a "larrikin" and "always a battler".
"Always looking for a cause he headed to Ukraine to drive trucks," she said.
Russia invaded Ukraine in February, with allegations of war crimes made against the federation's troops since the invasion.
During his trip to the Quad leaders' meeting on Tuesday, Mr Albanese said he had expressed Australia's view that the Russian "unilateral, illegal, immoral attack" on the people of Ukraine was an "outrage".
"The atrocities which are being committed on innocent civilians is something that we couldn't have expected in the 21st century," he told reporters after the meeting.
Earlier this month, then-foreign minister Marise Payne announced further sanctions on high-profile Russians, including media personalities and military higher-ups.