Hakeem Alaraibi, who plays for a semi-professional football club in Melbourne, was stopped by Thai immigration on November 27 after arriving in Bangkok for a vacation with his wife.
He is being held in detention, with a Thai court to rule next week on his fate.
Payne called for the 25-year-old's "immediate return" and said she had spoken to her Thai counterpart Don Pramudwinai.
"Australia is concerned by the ongoing detention of Mr Hakeem Ali Alaraibi and calls for his immediate return to Australia," she said in a statement.
"Australia has made, and will continue to make, high-level diplomatic representations seeking Mr Alaraibi's safe return."
The footballer said he was arrested and beaten at the start of the Arab Spring protests in the Gulf state in 2012. He was granted refugee status in Australia five years later.
Alaraibi was convicted in absentia on charges of vandalising a police station in Bahrain, but says he was out of the country playing in a match at the time of the alleged offence.
The office of Thailand's attorney-general on Friday submitted an extradition case to the criminal court on Bahrain's behalf as the Gulf state has an outstanding arrest warrant for Alaraibi.
Rights groups as well as FIFA, the international governing body for football, have called for his release.