Fire crews were called to a blaze in Sauchiehall Street’s pedestrian area at about 08:25 on Thursday morning.
Eight appliances were tackling the fire and police have closed the road at Hope Street.
Photos on social media showed smoke billowing from shop fronts opposite the former British Home Stores building on Sauchiechall Street.
Witnesses have described flames coming from the first floor of the building.
Hope Street has been closed to all traffic between Bath Street and Renfrew Street.>