A 66-year-old man was arrested in connection with the theft, but the golden toilet is still missing amid fears it may be melted down. On Saturday night, the man was being questioned by detectives.
The artwork had previously drawn huge crowds at New York's Guggenheim museum when it first went on display in 2016, and was later offered to Donald Trump in a satirical jibe at the President.
Blenheim Palace chief executive Dominic Hare said it is valued at about £4.8 million (NZD$9.4 million).
Its new home was a small stall adjacent to Churchill's birthing room, just off the Great Hall and near to the main entrance, where smashed glass was spotted. The thieves would have had to navigate the vast corridors to reach it.
Incredibly, Edward Spencer-Churchill, half-brother of the current Duke of Marlborough and founder of the Blenheim Art Foundation, told the Sunday Times last month: "Despite being born with a silver spoon in my mouth I have never had a s--- on a golden toilet, so I look forward to it."
Asked if he was worried about security, he said: "It's not going to be the easiest thing to nick".
"Firstly, it's plumbed in and secondly, a potential thief will have no idea who last used the toilet or what they ate. So no, I don't plan to be guarding it."
Home to the 12th Duke of Marlborough and his family, Blenheim Palace is a UNESCO World Heritage Site. It was built as a gift to John Churchill, the first Duke of Marlborough, from Queen Anne and a grateful nation in thanks for his victory at the Battle of Blenheim on 13 August 1704.
It was closed on Saturday, as police officers scoured the scene. In a statement, Palace officials said: "We are saddened by this extraordinary event, but also relieved no-one was hurt.
"If anyone knows or saw anything suspicious in connection with the event that may help us secure its return please contact Thames Valley Police."
At a press conference at the force's headquarters, Inspector Richard Nicholls said: "Thames Valley Police is investigating the burglary of a piece of art from Blenheim Palace in the early hours of this morning.
"A group of offenders broke into the palace and stole a high value toilet made out of gold that was on display.
"We believe they used at least two vehicles during the offence and left the scene at around 4.50am.
"The artwork has not been recovered at this time, but there is a thorough investigation being carried out."
They said officers first received a report of a burglary at Blenheim Palace in Woodstock, Oxfordshire, at 4.57am yesterday, adding that the offenders left the scene minutes earlier.
The Palace is set to open as usual on Sunday, with the rest of Cattelan's artwork on display until October 27.
This is the Italian's first solo exhibition in the UK in 20 years and features new works displayed for the first time.