An emergency call came in at 3.50pm and an ambulance and a senior paramedic officer were sent to the scene.
A West Midlands Ambulance Service spokesman said: “When crews arrived they found a Renault Clio upside down and a length of metal railings protecting a footpath badly damaged and bent.
“Thankfully, no-one was on the footpath at the time of the crash. Equally, it was fortunate that none of the railing entered the car.
“There were two adults and a child in the car. The 24 year old man driving was uninjured. The 20 year old woman front seat passenger had a head injury and cuts and bruising – she was assessed by ambulance staff and taken to University Hospital Coventry & Warwickshire.
“The 3 year old girl in the back was unhurt largely because she was well strapped into a good quality child seat; this undoubtedly protected her massively during the crash and should serve as a lesson to all parents with young children about the protection a child seat can provide.
“Whilst no-one would wish a crash like this on anyone, this could easily have been a much more serious incident.”