The incident happened outside West Mercia Police's headquarters in Monkmoor.
The HGV carrying shredded paper caught fire after its engine overheated.
Two appliances from Shrewsbury and a Shropshire Fire and Rescue officer attended the scene yesterday.
They spent nearly an hour tackling the blaze using a hose reel jet and two sets of breathing apparatus, as well as small gear.
No-one is believed to have been injured.