The owner of Koko Bean Aaron Forsgren, says there was a quick burst of flames as a pilot light for the gas stove was being lit.
Patrons who were in the restaurant, situated in the Laufou Shopping centre, say they heard an explosion coming from the back of Koko Bean.
The police say a woman who was lighting the pilot received second degree burns and another who was close by was also burned, but not as severe as her colleague.
They were injured shortly before noon on Christmas Eve.
Mr Forsgren says an inspector is arriving from off island to investigate and will reopen the restaurant once all inspections are complete.