The items were taken from an office which is located at the back of the cathedral.
The silver chalice is approximately seven inches tall and one of the silver plates is from the 16th Century, and is inscribed with 'St Anne's Parish Church Belfast'.
It is around five and a half inches wide, with the inscription on the underside, and a trumpet foot base which is dented.
The second plate is a copy of the first, but was made in 1894 and has an inscription 'The Parish Church 1895' on the underside of the dish.
Police said the theft was discovered at around 10.30am on Thursday.
They have appealed for anyone who noticed someone behaving suspiciously in the area of the cathedral on Donegall Street on either Wednesday or Thursday to get in touch.