Police said two males were seen breaking into the restaurant in Springvale, in Melbourne's southeast, about 12.15am on Sunday.
A spate of firebombings and arson attacks has swept the city in the past week, including an incident in which six cars were set alight at separate locations in a single night.
Fire crews arrived at the scene in the early hours of Sunday to find smoke billowing from the window of the restaurant.
The two males fled the scene in a car.
Shortly later, a teenage boy suffering burns was found at a fast-food restaurant in Heatherton, about a 10-minute drive from the Springvale fire scene.
Emergency services were called to the scene and treated the boy.
The 15-year-old was arrested and taken to hospital under police guard.
Police said a crime scene had been established and the investigation was ongoing.
Glass on the restaurant's door was smashed and a red jerry can was visible inside the property on Sunday as investigators pored over the site.
Days earlier, a 13-year-old boy was left fighting for life after suffering burns to 90 per cent of his body during an alleged firebombing in Taylors Hill.
The boy was found in a vehicle after what police believe was an attempt to flee the site on Thursday.
Police have since arrested two 16-year-old boys and a 15-year-old boy for questioning over the incidents.
The Taylors Hill incident was part of a busy night for investigators, who responded to reports of six cars being set alight in different locations.
Arson and Explosives Squad head Chris Murray said police were committed to finding others involved in the Taylors Hill arson and holding them responsible for the teen's injuries.
"We have a young boy whose life is currently hanging in the balance," he told reporters during the week.
"Let me be clear: this is not a game - no amount of money is worth risking your future or your life. Lighting a fire means putting yourself in danger."
Victoria has experienced a spate of arson attacks on vehicles, homes and businesses that police believe is linked to organised crime.
Criminal syndicates are suspected of recruiting young people online or via encrypted apps to carry out crimes on their behalf.
In September, a 23-year-old man was found in the car park of a tobacco shop with severe burns following an alleged firebombing in Melton, on the outskirts of Melbourne's northwest.
There have been more than 150 tobacco store fires in Victoria since March 2023.
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