The sculpture of the head of the Wedgwood pottery founder in Stoke-on-Trent was first unveiled in 1986.
Stoke-on-Trent City Council apologised unreservedly and said it had been removed by contractors during a road widening project.
Council leader Abi Brown said she was "devastated" the mistake had occurred.
A council spokesperson said they had launched an investigation into the error and were speaking with contractors to understand what had gone wrong.
The Josiah Wedgwood art installation, carved out of red bricks, was created by sculptor Vincent Woropay for the National Garden Festival in 1986.
It moved to its current location at Festival Park in 2009.
Local historian Fred Hughes, who attended the first unveiling of the sculpture, said it was "beyond belief" that it had been removed.
He said the remaining bricks of the sculpture should have been stored correctly so the sculpture could be reassembled elsewhere.
"As far as I'm concerned, it's a scandal and I want to see it repaired," he said.
The bricks and the base of the sculpture will now be sensitively removed from the park, the council had added.
"Culture is at the fabric of our city and plays a hugely significant role in the story of Stoke-on-Trent," Ms Brown said.
"I have instructed the director of the service to personally oversee immediate work to protect the sculpture and investigate how this has happened."