The inn was known first as the Fishes, then the Old Three Fishes and from 1838 to the present day as the Three Fishes. There are two possibilities for the origin of its name. The first is that it takes its name from the emblem of the Abbot of Lillishall Abbey whose town house stands on the corner at the junction of Fish Street and Butcher Row. The second and most likely is that the name reflects the fishmonger's trade that was carried out in the street from boards hung on the wall opposite and stretching from the Bear Steps to the junction with High Street. The fish market was held there on certain days of the week up until 1869 when it was removed to the new market hall at the top of Mardol.

The inn was officially recorded in 1780 and was one of four recorded in the street, the others being the Half Moon, the Plough and the Bear. The inn is housed in a picturesque half-timbered building, which has a jettied upper storey and probably dates from the 16th century.