The owners had installed a purpose-built 6ft (2m) high "wallaby-proof" fence, but staff at have been left scratching their heads after the 2ft (60cm) tall marsupial disappeared some time between Monday evening and Tuesday morning.
-> Two Yorkshire chippies named in UK's top 20 fish and chip shopsThe animal was one of two male Bennett's wallabies who arrived at the park on Monday.
It does not even have a name as the keepers were still in the early stages of planning a competition to name the new pair.
Animal manager Chris Holah said the family-run attraction had spent a lot of money on a specialist enclosure which they were assured by experts was wallaby-proof.
He said: "We're baffled, a bit embarrassed and obviously concerned.
"He's only been with us one day and he's just gone."
In a statement, the park said: "After spending the day settling in and a few close encounters with their neighbours, the rheas, they seemed to settle in well.
"They were last checked at 7.30pm last night and were happily in their shelter.
-> In Photos: The dramatic sinkholes which have opened up in Yorkshire"However at 7am today, when we went to feed them, it became apparent there was only one in there.
"After a very thorough search of the paddock, the park and surrounding area there was no sign of him."
The statement continued: "We can only assume he escaped, however the fence was built 2m high at great expense, specifically to keep the wallabies in.
"This was researched online months in advance and checked by several independent 'experts' and everyone was happy there was no way they could escape.
"There are no holes or obvious ways out so the whole situation is a mystery."
Mr Holah said the animal posed no threat to people and would probably be difficult to spot as he was likely to hide and was well camouflaged.
The local police helped with this tweet: "G'day mate there's a lost Wallaby from Filey Bird Garden and Animal Park, Scarborough Road, Filey. If seen please ring us on 101. Thanks."