Fire crews were called to the fire at Belair Avenue in Glenroy about 4.50am.
Investigators have been told three offenders were seen pouring what appeared to be an accelerant on the truck before setting it alight.
Police said the trio fled the scene.
A crime scene has been established, and the fire is being treated as suspicious.
Investigators will examine potential links to other recent fires. The motive remains unclear, including whether the nearby tobacco store was the intended target.