If the faucet is attached to the house, i would think the shut off valve would be in the crawl space or in the basement. If in fact the shut off valve is inside a wall it could cause a lot of damage if a leak ever developed. Maybe some one else will be along with a better idea of what to do.

There is no crawl space because we're on a slab.

If you want to use the facuet your option is to tear in from outside to see what needs to be done. From your skimpy discription,I assume it is a frostproof facuet coming through a brick wall. I would expect the supply to come out of slab through bottom wall plate within 6" right or left of facuet. I wouldn't expect to find a valve in the wall unless someone added it after house was built. A shot in the dark is that the facuet froze because a hose was left attached in cold weather. The wall was cut from inside to alow capping the supply and repair was never completed.