Emergency services closed a slip road onto the roundabout, at junction 28 of the M62, after a collision between two cars shortly after 2pm.
One man was taken to Pinderfields Hospital with a suspected wrist injury.
The slip road has since reopened but bus users have been warned to expect delays, with the 47, 48, 48A, 117, 202 and 203 routes all affected.
A spokeswoman for West Yorkshire Police said: "We were called at 2.06pm to Dewsbury Road, near to the Tingley roundabout, to reports of a two vehicle road traffic collision. The vehicles involved were a black Range Rover and a black VW Golf.
"One of the slip roads onto the roundabout was closed and reopened at 3.23pm."