It was taken from public display from Leeds Castle between November 10-14.
The vase (also described as a goblet by Kent Police) has been valued at around £1500.
Anyone who witnessed the item being stolen, knows where it is, or is offered it for sale, is urged to call the appeal line on 01622 604100.
You can also call the independent charity Crimestoppers anonymously on 0800 555111.
Kent Police has not issued a crime reference number.