Management officials at Dalscone Farm Fun in Dumfries said five boys chased the park’s three wallabies around their enclosure on Saturday evening.
Two of the animals escaped the enclosure but the third, a baby named Mick, was so shaken it died on Sunday evening.
He was treated by a vet but did not survive, the park said.
It was said the group of boys had been “causing havoc” at a nearby garden centre before chasing the wallabies.
Police Scotland have been informed and officers visited the farm on Monday morning.
A statement on the Dalscone Farm Fun Facebook page said: “They let two of them out of their enclosure and the third was so traumatised it died on Sunday evening.
“Does anyone know who they are? They had been causing havoc at Heathhall garden centre before heading here.
“It all happened between 5.50pm and 6.50pm. Any information would be greatly appreciated, please call 101 to let police know any potential leads.
“Thanks to Alistair from Nithsdale vets for all his hard work to try and save Mick our baby wallaby.”
The park has an indoor play centre and collection of animals including llamas, donkeys and ponies.
The outdoor farm park was due to open in April.