More than 20 firefighters were sent to the Westmorland Shopping Centre in Kendal just after 08:00 BST when smoke was spotted by a member of staff.
A cordon was put in place around the split-level complex, which houses about 30 shops and an indoor market.
A fire service spokesman said the blaze was quickly extinguished and no-one was injured.
He said the site would remain closed for a time for smoke to be ventilated from the building.
A Cumbria shopping centre had to be evacuated after a fire started in a shop storeroom.