South Yorkshire Police said there was ‘at least one fight’ in Endcliffe Park last Saturday night and an investigation is under way.
The force wants mobile phone and CCTV footage, plus witnesses are also being urged to come forward.
Residents and park users have complained to the police about crowds gathering on the grass, anti-social behaviour and the use of drugs.
The Sheffield South West neighbourhood policing team said: “We have been in the park and on Rustlings Road speaking with local residents and park users. We will be increasing our patrols of the park.
“We are aware of the anti-social behaviour and the use of Nitrous Oxide canisters in the park. We will work with our partners to tackle this issue.”
Slate Powell, posting on Facebook yesterday, said: “I went for a walk there this evening and it’s totally rammed - no social distancing at all, loads of drug use, rubbish everywhere.
“It feels genuinely unpleasant and threatening, such a different atmosphere to previous years.”
Fran Grainger-Leigh added: “It’s good that this has been recognised now but it needs a police presence late afternoon and into the evening. “That's when people are dealing and taking drugs in what should be a family friendly place.”
Witnesses or anyone with footage of any fights in Endcliffe Park on Saturday, June 20, should call South Yorkshire Police on 101.