One girl sustained a minor injury to her hand in the fight which occurred on Link Walk, in Eastfield, between 3.10pm and 3.30pm on Wednesday March 7.
Three people have been arrested including two girls aged 15 and 17 and a woman in her 40s.
The 17-year-old girl and the woman have been released on bail while enquiries continue, and the 15-year-old has been released while under investigation.
Police are appealing to anyone who witnessed the incident and has any mobile phone footage to contact them, rather than share it on social media.
A spokesperson for North Yorkshire Police said: "Anyone who can assist the investigation on asked to contact North Yorkshire Police on 101, select option 2 and ask for Scarborough Investigation Hub.
"If you wish to remain anonymous, you can pass information to Crimestoppers on 0800 555 111.
"Please quote reference number 12180039433 when passing on information."