Four of the injured 'sadhus' were admitted to the district hospital, while the two others, hurt in the clash during which sharp-edged 'trishuls' (tridents) were used to attack each other, were treated at the Akhara, Additional Superintendent of Police Manish Khatri told PTI.
Two sadhus have been arrested in connection with the incident, police said.
According to some pilgrims, loud sounds of gun shots were heard during the clash which took place at 'Ahavan Akhara' (temporary monastery).
A case was registered and further investigations are on, the ASP said.
The clash is suspected to have taken place over elections for different posts in the Akhara, police officials said.