A One Nation campaign vehicle has been set alight in a shopping centre on Hobart's eastern shore, less than 24 hours after the federal election.

The truck was reportedly being driven by Tasmanian One Nation Senate candidate Adam Lambert who was buying groceries in a shopping centre when the blaze broke out.

A bar attendant at the nearby Shoreline Hotel in Howrah said she saw flames erupting from the car park and called police shortly after 5:00pm.

Three fire crews from the Tasmanian Fire Service arrived on scene to extinguish the blaze.

Tasmania Police said the fire looked to be "suspicious" and investigations into what caused the blaze had begun.

Responding on social media, One Nation leader Pauline Hanson blamed the "left" and said "someone was seen torching it before fleeing.

"It is amazing how the left call for tolerance but act like they're above the law when you don't agree with their ideologies," she tweeted.

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Shoppers in the area say they heard an explosion that "sounded like a petrol bomb."

The campaign vehicle features a billboard of Pauline Hanson and two Tasmanian Senate candidates Adam Lambert and Mathew Stephen.

Police are calling on anyone who witnessed the blaze to contact Crime Stoppers.

The burnt aftermath of a One Nation campaign car left abandoned in a deserted shopping centre carpark on Hobart's eastern shore. ( ABC News: Phoebe Hosier )