The carved bear's head, runic inscription and Medieval cross slab were part of a collection at All Saints Church in Sockburn.
They date from the 9th to 10th Century and are described as being "of national importance".
It is not known whether they were taken by "someone with a genuine passion who thought they might look better elsewhere" or to be sold, police said.
All Saints Church dates from the Norman Conquest.
By the 19th century it had become a ruin and landowner Sir Edward Buckley had part of it reconstructed "for the reception and preservation of the ancient stones lying among the ruins," the Diocese of Durham said.
A spokesperson added: "Many of our churches... have items of historical importance and making them available to our communities is clearly part of our open door policy.
"However, that is no excuse for the wanton removal of any items as this is a crime which affects the whole community."
It is unclear when the carvings went missing, as the grounds are open to the public.
Three Viking stone carvings have gone missing from a County Durham church.