Police, fire and ambulance services rushed to the park at Milngavie after being alerted around 12.20am.
The 18-year-old man was taken by air ambulance to the Queen Elizabeth University Hospital in Glasgow as a precaution.
Five other young people in his group were found safe and well by the rescue teams.
A Police Scotland spokesperson said: “Emergency services attended and an 18-year-old man was conveyed to Queen Elizabeth University Hospital by helimed as a precaution.
“Five other persons were traced safe and well.”