The incident happened at Dalscone Farm Fun in Dumfries on Saturday night after the park's three wallabies were chased around their enclosure by five boys.
Two of the animals escaped the enclosure but the third was so shaken it died.
Police Scotland confirmed in a short statement that a 16-year-old boy had been arrested.
It added that inquiries were continuing into the incident but thanked the public for their assistance with the investigation.
A teenager has been arrested following the death of a wallaby at a farm play park in the south of Scotland.