The 15-year-old was attacked in Pollok after becoming involved in an argument with another youth.
It happened in Brockburn Road, near to Levernside Crescent, at around 10pm on Thursday.
The culrpit - who has shoulder-length hair and earrings in both ears - ran off towards Crookston Castle.
He was wearing a navy blue hooded top and black trousers.
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.
"We have managed to speak to some of the youths but I belive 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.