Police are investigating after a window of the cabmen's shelter in Market Square was smashed.
The building, which was used by drivers of horse drawn cabs waiting for fares, is one of only a handful left in the country.
The rare shelter was provided in 1911 through a legacy of £200 by Sarah Carter, the daughter of a former mayor of Ripon.
It was a prefabricated building by Boulton and Paul, a Norwich firm which also provided huts for Scott’s 1910-13 Antarctic expedition.
In 1980 the Royal Engineers restored it and fitted it onto a wheeled chassis to allow it to be moved.
It has since been restored twice after becoming badly decayed.
Police believe the building was targeted some time between March 12 and March 15.
Officers are asking for the public's assistance to help narrow down the time when the damage occurred and to identify those responsible.
Anyone with information can call North Yorkshire Police on 101, quoting reference number 12210080826.