A gang broke into the Oxfordshire palace at about 04:50 BST and stole the artwork, Thames Valley Police said.
The working toilet - entitled America, which visitors had been invited to use - has not been found but a 66-year-old man has been arrested.
The burglary caused "significant damage and flooding" because the toilet was plumbed into the building, police said.
It was part of an exhibition by Italian conceptual artist Maurizio Cattelan that opened on Thursday.
