They were called to Marshfield Road at around 3.30am to reports of an incident involving several people.
A 36-year-old man suffered serious hand injuries and was taken to hospital for treatment.
A 23-year-old man has been arrested on suspicion of GBH and is in custody for questioning.
Investigating officer Det Con Ben Sullivan said: “We believe there may be more people involved in this disturbance who we haven’t yet spoken to and I would encourage them to come forward.
“We aren’t treating this as a random incident and believe the people involved were known to each other. We have a scene watch in place to preserve evidence as part of our ongoing investigation.”
If anyone saw the disturbance, or has information which would help the police they are asked to call Bristol CID via the 24-hour Police Enquiry Centre on 101.