Alaska, an American bald eagle, is thought to have bitten through his tethers, before flying off from World of Wings in Cumbernauld.
The highly distinctive bird, which has a 7ft wingspan, left his shelter before heading into woods a mile away.
He was last seen on a treetop at Tannoch Stables near Palacerigg Country Park.
The centre's director David Ritchie said: "There were 60 children watching a buzzard flying display when Alaska swooped across the flying area, circled a few times then sat on a pole. He then took off and disappeared in to the distance.
"We chased him up to a wooded area about a mile from the centre, but lost sight of him in the trees."
Alaska was hatched in Holland in 2006 and brought to Scotland five years ago. He has never had to hunt for himself.
Mr Ritchie added: "Because he wasn't flying, Alaska was given extra food so he won't need to come down for food for a few days.
"When he gets hungry he may scavenge, but I don't think he'd be able to hunt for live food.
"My greatest fear is he'll be mobbed by crows. Because of his size, crows will see him as a predator. So we need to get him back as quickly as possible."
He said Alaska was unlikely to approach people, adding: "He's quite a nervous bird. He'll most likely find somewhere to roost and stay there.
"We would ask people not to spook him.
"If anyone sees him, they should just get in touch with us and someone will be out immediately."
Like all American bald eagles, Alaska has a vast wingspan, white head and tail.
Anyone who sees Alaska is asked to call World of Wings on 01236 722 999.