South Wales Fire and Rescue Service was called to the Butetown tunnel just after 01:00 BST.
Two crews from Cardiff Central, two from Ely and a crew from Penarth went to the scene.
South Wales Police said the A4232 westbound tunnel remained closed after parts of it were damaged in the crash.
A spokesman for the Welsh Ambulance Service said the woman had been taken to Cardiff's University Hospital of Wales with unknown injuries.
A woman has been taken to hospital following a crash in Cardiff in the early hours of Monday morning.