On arrival the group had already made off from the area.
No injuries have been reported and no-one has been arrested at this stage.
However, following an initial search of the cemetery, a number of weapons have been recovered, including knives.
Further searches are due to take place on Thursday morning A scene guard and temporary cordon has been put in place overnight to keep people away from the cemetery while these enquiries are on-going.
Chief Inspector Mark Grange, from North Yorkshire Police, said:
This is clearly a very concerning incident due to the apparent use of weapons, including knives. We are doing everything we can to investigate the full circumstances and, ultimately, trace those involved in the fighting.
While these enquiries continue, police patrols have been stepped up in the area to provide a visible and reassuring presence in the community. We realise the temporary closure of the cemetery may cause some upset with local residents, but we are aiming to keep this disruption to a minimum by completing the searches as soon as possible.
Witnesses to the incident or anyone with information that could assist the investigation, are urged to contact North Yorkshire Police on 101, select option 1, and speak to the Force Control Room.
If you would prefer to remain anonymous, please call Crimestoppers on 0800 555111.
Please quote reference NYP-17022016-0216 when providing details about this incident.