Member of Parliament Eric Abetz said two guards hired by the immigration department were asleep on the job when 25-year-old Carlo Konstantin Kohl escaped through an emergency exit in the transit area of Bangkok's international airport on May 15.
The connecting Thai Airways International flight in Bangkok to Frankfurt was delayed, and Kohl managed to flee on the pretext of taking a shower.
Thai authorities said they believe Kohl is on the run in Thailand and have posted a reward for his capture.
He had been convicted of theft and other charges in Australia and was reportedly released after serving three years. Convicts are routinely deported when they complete their sentence.
Thai officials said they were not informed that a German criminal escorted by Australian guards was passing through Bangkok.
"Nobody informed us beforehand of the suspect's arrival, which would have been normal procedure," said an airport official who asked to remain anonymous. "They only contacted us after he had disappeared."