Announcing the move, Home Affairs Minister Peter Dutton described Prakash as "a very dangerous individual".
Intelligence officials say Melbourne-born Prakash was a recruiter for the Islamic State (IS) group and encouraged terrorist plots in Australia.
He is currently being held in Turkey where he faces trial on terror-related charges.
In July, a Turkish court ruled against extraditing him to face terrorism charges in his home country.
In Australia, he faces charges of being member of a terrorist organisation as well as supporting and promoting IS.
In a televised new conference, Mr Dutton said Prakash had been central to IS's efforts in the Middle East.
"If given the opportunity Mr Prakash would harm or kill Australians and our country is a safer place for him having lost his Australian citizenship," he said.