The incident happened at about 6am on St Ladoc Road, near the junction with Bristol Road.
Police say a car appears to have hit a roadside wall and the two occupants – a male driver and a female passenger – were trapped.
They were released and taken to Southmead Hospital with possible life-threatening injuries.
The road remains closed to allow collision investigators to make a detailed examination of the scene.
Anyone who was in the area at the time of the incident and may information to help police inquiries is asked to contact the collision investigation unit on the force number 101.