Firefighters and paramedics were called to Leeds Road, near Pool in Wharfedale after two cars collided at 10.30am.
A man and a woman were trapped inside a vehicle following the crash.
A West Yorkshire Fire and Rescue Service spokesperson said another man was also injured but was already outside his car when they arrived.
Fire crews from Rawdon, Otley and Cookridge were called to the scene and freed both people who were trapped.
The spokesperson said all three people were taken to hospital.