Emergency services were called to Albion Street following the collision at Wormald Row, near to The Light shopping centre.
West Yorkshire Police said one man had been injured, although the injuries were not serious or life-threatening.
A spokeswoman for the force said: "We were called by the ambulance service at 10.32am to reports of a two-car road traffic collision.
"One male is being treated for wrist injuries."
Police said there was no more information on whether the man injured was a pedestrian or in one of the cars.
Traffic on Albion Street may be impacted as a result of the collision.