At about 18:30, the company stated it looked like the fire had started from the open fire in the pub and some firefighters were still at the site.
But the fire had not spread anywhere else in the building, it added.
The firm said it was awaiting contractors to check over electrics and gas pipes and start repairs.
The building was originally Market Drayton’s first purpose-built cinema, which opened in 1927 and closed in 1966. It later became a bingo hall and then a supermarket.
The fire service had said police were also at the scene and asked people to avoid the area and close windows and doors to avoid smoke.
Eight appliances were mobilised from Hodnet, Market Drayton, Prees, Shrewsbury, Wem, and Whitchurch.