Ambulance crews at the scene at the A456 Hagley Road West in Birmingham said it was "astonishing" those inside were not more seriously hurt.
The children, aged five and six, were taken to Birmingham Children's Hospital, the man went to Queen Elizabeth Hospital.
Their injuries are not thought to be life-threatening or life-changing.
Photos tweeted by West Midlands Ambulance Service show the car mounted the pavement and smashed through the barrier on the island above the road in Quinton.
The accident happened at about 22:30 BST on Saturday.
A man and two children had a "miraculous escape" when the car they were in plunged off a flyover.