Robert Edward Cerantonio, 29, who also goes by the name Musa Cerantonio, was detained in the central city of Cebu on Friday and will be deported to Australia, Philippine police said.
A report in The Australian newspaper described Cerantonio as a preacher and "one of (the Islamic State's) most influential propagandists", but Bishop belittled the Melbourne native.
"It seems that he is just a fraud, because he was saying that he was fighting in Syria and Iraq when all the time he was holed up in a flat in the Philippines," she told Sky News.
"So presumably he's a fraud who has tried to dupe people into this dangerous activity. What happens to him will be a matter for the authorities."
Cerantonio was arrested at the request of the Australian government and will be deported because Canberra has cancelled his passport, making him an illegal alien, Philippine officials said.
The Philippines has a large Muslim minority in the southern region of Mindanao, a hotbed for a decades-old Muslim insurgency and where Islamic militants linked to Al-Qaeda also operate.
But Cebu's police commander, Chief Superintendent Prudencio Banas, said there was "no evidence linking him to any terror act".
Police said they had been monitoring his activities since February when he arrived in Cebu, the country's largest metropolis outside Manila.
He lived with a Philippine woman and moved around Cebu until his arrest at a one-room apartment near the airport.