It is not known if he is still in custody.
Gardiner, 43, served as an Australian Army combat engineer in Somalia in the early 1990s, the ABC reports.
Attorney-General George Brandis' office has previously said citizens fighting illegally in overseas conflicts could face up to life in prison on their return to Australia.
"It is illegal to fight in Syria for either side of the conflict," a spokesman said.
"If you fight illegally in overseas conflicts, you face up to life in prison upon your return to Australia.
"We know there are some Australians who think they've made the right choice in becoming involved in overseas conflicts, but that choice only adds to the suffering in Syria and Iraq and it's putting those Australians and others in mortal danger."
Although the Australian Defence Force and Kurdish rebels may share a common enemy, the Australian Government does not recognise the Kurds as a legitimate armed force in Iraq.
Gardiner was stood down as president of the NT Labor Party and had his membership suspended after leaving.
- AAP