The altercation happened after a crash in Halesowen Road, Cradley Heath, on Sunday evening.
The collision involved three cars and happened next to a disused speed camera outside the Haden Cross Inn at around 9.30pm.
Emergency services were called and a man was arrested on suspicion of assault and driving while unfit through drink or drugs.
One of the drivers was also taken to hospital after being checked over.
A spokesman for West Midlands Police said: "A 32-year-old man has been arrested on suspicion of assault after another man was bitten on the arm following an altercation.
"It happened following a three-car collision in Halesowen Road just after 9.30pm. The suspect was also arrested on suspicion of driving while unfit through drink or drugs and remains in custody for questioning."
Crews from West Midlands Fire Service arrived within five minutes of being called. One man had freed himself before the firefighters arrived and made all of the vehicles involved safe.
A spokesman for West Midlands Fire Service said: "We had the call at 9.37pm to a road traffic collision on Halesowen Road in Old Hill. One fire engine and one brigade response vehicle responded – they were from Haden Cross fire station and they were on the scene in around four minutes."
Meanwhile one ambulance and a paramedic officer were sent to the scene. One patient, a man and a driver of one of the cars, was taken to hospital after being checked over.
A spokeswoman for West Midlands Ambulance Service said: "On arrival, we discovered one patient, a man, who was the driver of one of the cars, he was assessed and had sustained minor injuries and was conveyed to Russells Hall Hospital for further treatment. The other drivers were uninjured and discharged on scene."