Shaun Jobson, director of education at Bill Quay farm found Sloane the Pekin duck, loved by visitors, was missing when checking on her pen.
The door, which can only be unlocked manually, was found wide open on Sunday morning.
Down the road in Hebburn, Aaron Whitehouse was told by his parents they were unable to find four ducks he kept on his allotment in South Drive.
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All five ducks had been taken overnight on Saturday June 25.
Mr Jobson, who has informed police, said: “Sloane is loved by everyone who comes to see her. People come to talk to her. We have children come to the farm and they take part in feeding the animals, and Sloane is really popular with the children.
“All the animals mean a lot to the young people who come to the farm. We have all been left devastated by her disappearance.”
Sloane was left locked in her pen at about 10pm on Saturday by staff, but by Sunday morning the duck, aged two, had gone.
Mr Jobson added: “We put a post out on Facebook asking people to get in touch with us, if they see her and there has been a few possible sightings. We have had four ducks, that don't belong to us handed in, that were found wandering the streets, but as yet we have not found Sloane.”
The police have been informed.
Mr Whitehouse, 24, was told by his parents Joe and Tracy Whitehouse his four ducks were missing, believed to have been stolen, when they visited the site on Sunday morning.
It is the second time Mr Whitehouse from Mons Avenue, Hebburn, has had his animals targeted after finding a number of chickens had been beheaded six-months after moving onto the site.
It is believed the ducks, all aged seven-months, were taken overnight on Saturday - the same night Sloane went missing from Bill Quay farm.
Mr Whitehouse said: “I am just getting sick of it. This is the second time my animals have been targeted. I had some little white chickens which were killed and hoyed across the garden, six months after taking over the garden.
“And now someone has come in and taken my ducks. I'm just fed up. I haven't reported it to the police, as I don't see the point."
His dad Joe, 61, said: “If it had been a fox there would have been carcasses left behind. But it looks like someone has climbed over the fence as they have trampled over the onions to get to the ducks.”
Mr Whitehouse does not plan on replacing the ducks and has not reported the incident to police.
It is not the first time Mr Whitehouse has made the news.
A Northumbria Police spokesperson said: “We are investigating the theft of a duck from Bill Quay Community Farm. It is understood that an offender has entered the farm between 10pm on Saturday (June 25) and 9am on Sunday (June 26). They have then removed a duck from the paddock and left the scene.
“Inquiries are ongoing and anyone with information is asked to contact police.”
Anyone with information can contact police via the ‘Tell Us Something’ page of the Northumbria Police website or by calling 101 quoting crime number 075765R/22.