Smoke plumes filled the air after the fire broke out on a property on Pembroke Street, Old Town, and emergency services arrived at the scene at 5 p.m.
A local has shared video footage of the fire with Adver.
The fire is believed to have been extinguished about 45 minutes later at 5.45pm and people are commenting on social media that no one appears to have been injured.
Wiltshire police confirmed they were attending to support 999 comrades and the road was cut off as the fire was extinguished.
Dorset and Wiltshire firefighters and rescue have received an update.