Yes, but not in the same places or for the same reasons where most shave these days. Most people went about covered from the neck down, and usually women also covered their hair, so there was little reason to shave legs or arms: Women did proably luch facial hair, and for a certain period of time they shaved hregularly the head and brow producing an extremely high forehead. On the naked forehead they would sometimes apply white lead make up too.
Prostitutes sometimes went one step further, and shaved their vulva. This small statues was placed over the rebuilt Porta Tosa in Milan. This is the door through which Frederick I Barbarossa assaulted and raided the city.
According to the tradition the statue depicts either the young prostitute that stopped the assault of Frederick’s army by shaving her pubes in plain view, or Frederick’s wife acting as a prostitute.