The 15-year-old was attacked in Pollok after becoming involved in an argument with another teenager.
It happened in Brockburn Road near to Levernside Crescent at around 10pm on Thursday.
The culrpit - who is had shoulder-length hair and stretched earrings in both ears - ran off towards Crookston Castle.
He was wearing a navy blue hooded top and black trousers.
Police said the victim was rushed to the Southern General Hospital, where he is in a "serious but stable" condition.
Detective Constable Lauren Docherty from Greater Glasgow CID, said: "The park was very busy at 10pm on Thursday.
"Although we have managed to speak to some of the youths within the park at this time, I believe there are many more we still have to speak to.
"I urge anyone who has not yet spoken to police to contact us immediately."
Anyone with information is asked to contact Police Scotland on 101.