One appliance and crew from Buckingham, one from Leighton Buzzard and an officer attended.
Firefighters released a woman, injured, and left her in the care of South Central Ambulance Service. A girl and a man were also injured but not trapped.
The road was temporarily closed in both directions. It is not known when it will reopen.
Firefighters used an environmental protection kit to prevent vehicle fluids from entering the water course.