Captain Ari Sapari, director of operations for Garuda, said the authorities were trying to rescue passengers on board the Boeing 737-400.
Bambang Susanto, Jogyakarta's provincial secretary, said the jet "overshot the runway and burst into flames".
Hariman, a witness, told a local radio station that "the fire came suddenly from the front wheel".
A spokesman for the Australian department of foreign affairs and trade said Australian government officials and journalists were on board the jet but there was no word yet on their fate.