Police confirmed they had arrested one suspect, a male, in connection with the stabbing which occurred at around 2.30pm on Saturday.
According to West Yorkshire Police, the victim was involved in an altercation in Kirkgate and tried to flee but he was chased by another man.
Whilst fleeing the scene, the victim collided with a silver BMW 730 and he was then stabbed multiple times.
The victim was taken to Leeds General Infirmary and is receiving medical treatment.
There was a heavy police presence in the centre of Shipley yesterday afternoon - on a busy market day for the town.
Officers cordoned off an area near Shipley Town Hall, where the attack is believed to have taken place, and traffic was being diverted.
A team of around eight police officers were investigating the cordoned-off area, within which were parked two cars.
One eye-witness said that the nearby bowling green was evacuated to allow an air ambulance to land.
It is believed the injured man was then airlifted to hospital.