The burglary caused “significant damage and flooding” because the toilet was plumbed into the building.
The fully-functioning piece by Italian artist Maurizio Cattelan, dubbed “America”, was once displayed at New York’s Guggenheim museum and offered on loan to US President Donald Trump.
It was part of an exhibition by Italian conceptual artist Maurizio Cattelan that opened on Thursday.
A 66-year-old man has been arrested over the theft at the 18th-century stately home in Oxfordshire, a World Heritage Site and the birthplace of Sir Winston Churchill.
It is currently closed while investigations continue.