The minibus towing a car overturned on the embankment on the southbound carriageway near junction nine for the A34 at around 8.10pm.
All nine people on board were able to free themselves from the minibus which was severely damaged.
Two adults and a child aged between four and seven sustained serious injuries, according to the ambulance service.
While the others - two adults, three children, also between four and seven years-old, and a baby - suffered minor injuries and all nine were taken to the John Radcliffe Hospital.
Bicester Fire Station watch manager Pete Mackay said: “This incident shows that accidents can happen anytime, and it is extremely fortunate in this instance that all the people involved were able to be freed unaided from the vehicle.”
Thames Valley Police is investigating the cause of the incident.
Four fire engines, including the specialist rescue crew from Kidlington, police, five ambulances, two officers in rapid response vehicles, an emergency doctor and the Thames Valley Air Ambulance emergency response vehicle were all sent to the scene.