The truck, a 1986 Nissan Atlas, was taken from The Glen about 4.30am.
Police would like to speak with two men who were seen at the Night and Day store in the Octagon yesterday morning about 5.25am.
They entered the store and left separately after a short time before getting into the truck and heading north.
Police are also asking members of the public to report any sightings of the truck.
Its registration number is TR9930.
There were several sightings yesterday of the truck heading north on State Highway 1 towards Christchurch.
Anyone with information should contact their local police station.
Alternatively, information can be provided anonymously via Crimestoppers on 0800 555 111.