Edinburgh City Council said "a number of complaints" had been made about the cow protruding from the West End eatery Kyloe Restaurant and Grill in the two years since it was erected without permission.
The restaurant owner of Kyloe, which is said to be an old Scots word for cow, is to launch a campaign to save the sculpture it is claimed is "practically an Edinburgh landmark".
The council said it was willing to discuss the issue with the restaurant.
Nic Wood, owner of Signature Pub Group, said: "What harm is it doing? So many customers find us by the cow, love the cow, discuss the cow, are mesmerised by the cow. It's a poor show the council now asks us to take it down."
He said the cow had helped customers find the restaurant during tram work disruption.
Mr Wood added: "The inconvenience caused by the execution of the tram works, over the last few years have lost us so much business, because people couldn't find us and couldn't get to us.
"Our cow was a means of overcoming this by raising our profile during times of adversity."
The firm was given 21 days to take down the cow, and the deadline is Boxing Day.
A council spokesman said: "Following a number of complaints about this sculpture, we have written to the owners of Kyloe Restaurant and Grill advising that because Listed Building Consent has neither been sought nor obtained for this feature, we have no option but to request its removal.
"We would of course be happy to discuss the issue with the owners."