Police were called to a green space in the park at around 4.30pm on Friday after reports of an incident involving a “large number” of people.
Two boys, both aged 16, are currently being treated at the Queen Elizabeth hospital for cuts and concussion following the incident.
On Saturday, Police Scotland confirmed that four teenagers, aged 14-17, were arrested and charged with public order offences.
The 17-year-old boy was also charged with assault.
Earlier on Friday, police had posted on social media urging people to enjoy the park “responsibly”, saying that weather was forecast to be “nice” over the weekend and that extra patrols would be in place.
Temperatures in the city on Friday peaked at 21.9C (71.4F) at around 2.30pm.