Police were called to Armley Ridge Road at 3.20pm today (Thursday) after reports of the collision.
The man suffered a serious head injury and was airlifted to Leeds General Infirmary where he is now being treated.
His injuries are not thought to be life-threatening, police said.
Motorists travelling in Armley faced heavy delays as road closures were in place at Armley Ridge Road and Gotts Park Avenue after the incident.
The roads have now reopened.