The animal was left seriously injured by the incident at Lakelands near Craigavon.
Eyewitnesses reported the goose was flapping around and crying in pain after being attacked by two youths.
The PSNI has appealed for information.
Details of the incident have been posted on the Save Craigavon City Park & Lakes Facebook page.
The post said: “(On Friday) at approximately 3.30pm close to Lakelands, two young lads who looked in their teens impaled a goose with some sort of white pole.
“They ran off when interrupted by a resident.
“The goose was last seen in the middle of the lake flapping around and crying out with the pole still attached and then all went quiet.
“The USPCA and the police have been informed.
“The males were white, with dark hair, looked curly-ish, and we believe they had a smallish dog with them and one was carrying a blue rope.
“We assume they must have brought the white pole with them too so they may have been carrying that around with them. They ran off towards the leisure centre.”
The post urged anyone with information on the incident to contact police or the USPCA.
It added: “These geese are a protected species and any attempt to harm them is a criminal offence.”
The USPCA said it was “shocked and appalled by this senseless act of cruelty”.
Chief executive Nora Smith said, “This is a horrific, sickening case of animal cruelty and we are appalled to hear of such barbaric abuse.
“We cannot comprehend the motives of anyone who can carry out such a brutal attack against a vulnerable animal.
“There can be no justification for this criminal behaviour, and we hope that the perpetrators are brought to justice swiftly.
“Unfortunately this is another stark reminder of the many challenges we are still facing with regards to animal welfare in Northern Ireland.”
A PSNI spokesperson confirmed the incident was being investigated by officers.
They said: “Police received a report of youths attacking and seriously injuring a goose in the Lakelands area of Craigavon shortly before 4pm on Friday May 17.
“Enquiries are ongoing and anyone who may have witnessed the incident or anyone with CCTV or other footage that could assist police is asked to get in touch on 101 quoting reference 1162 of 17/05/24.”
William Turner is a seasoned U.K. correspondent with a deep understanding of domestic affairs. With a passion for British politics and culture, he provides insightful analysis and comprehensive coverage of events within the United Kingdom.