South Lakes Wild Animal Park owner David Gill, 53, had denied personal responsibility for letting a sacred ibis fly from the zoo near Dalton-in-Furness to nearby beaches three times.
But he was fined Â£2,000 at Kendal Magistrates' Court and the company was fined a further Â£5,000.
Gill was convicted of three offences under the Wildlife and Countryside Act.
The birds, from Africa, are the size of a heron, with large beaks and voracious appetites. They are on a list of species the authorities do not want settled in the UK.
Andy McWilliam, from the National Wildlife Crime Unit, said the birds cause significant damage in the wild.
"If a sacred ibis goes through a tern colony it'll just take all the eggs, all the chicks, they basically eat anything in their path," he said.
The birds are supposed to have their wings clipped, or surgically treated, to stop them flying away.
Gill did not comment following his conviction.
An animal park owner in Cumbria has been fined for allowing a "threatening" bird to escape.