Footage of the attack on a fast-food outlet in the southern city of Melbourne showed two people in dark hoodies and trousers with a container of what police described as "flammable liquid".
One of them tried to set the fluid alight at the front of the outlet, just out of the view of a camera.
In an instant, the arsonist is seen again engulfed in flames and then hurriedly removing the burning trousers before running off bare-cheeked with an apparently unharmed accomplice.
Victoria state police, who distributed the footage on Thursday, asked for witnesses to the attack, which happened in the early hours of Christmas morning.
"Investigators have released CCTV and images of two people they believe may be able to assist with their enquires," they said in a statement.
