A silver Toyota Corolla taxi travelling east on Ladgate Lane collided with a silver Chevrolet Aveo and a silver Mercedes E Class travelling west.
A 72-year-old woman who was a passenger in the rear of the taxi sustained broken arm and was taken to James Cook University Hospital and released following treatment.
The 64-year-old driver of the taxi was arrested at the scene on suspicion of failure to provide a specimen, causing serious injury by careless driving and driving whilst unfit.
The drivers of the other vehicles were not seriously injured.
Those with details can call Middlesbrough Police on 101 and quote Reference Number: SE24106000.
Alternatively, if those wishing to remain anonymous and want to help police with the investigation can do so by giving information to the independent charity CrimeStoppers on 0800555111.