Around 8.15pm a 24-year-old man was assaulted by a man with glass bottle.
The victim was then chased towards Waverley Park by a group of men where he was assaulted again, said police.
The victim was taken to Glasgow Royal Infirmary for treatment to his injuries.
The suspect involved in the initial assault is described as wearing dark clothing.
Detective Sergeant Craig Paterson from Kirkintilloch CID said: “The skate park was busy at the time of this assault and I would appeal to anyone who witnessed what happened, or noticed the subsequent incident in Waverley Crescent, to please get in touch.
“Anyone with information is asked to contact Police Scotland through 101, quoting incident number 3373 of Saturday, 26 June, 2021. Alternatively you can call Crimestoppers anonymously on 0800 555 111.”