The accident happened at around midday with Garda saying the woman was a passenger on the Luas when it crashed into the car near the Hospital stop.
The woman’s injuries are not believed to be life-threatening and she was treated in hospital.
Luas operators, Transdev, said services between Belgard and Tallaght were closed with trams only running from The Point/Connolly stops to Belgard/Saggart stops.
It said alternative bus services are running to all stops between Belgard and Tallaght.
Gardaí have asked anyone who witnessed the collision to contact Tallaght Garda station on 01 6666000.