The three were travelling in a Honda Accord coupe towards Dunedin on Three Mile Hill Rd about 10.10am.
Senior Sergeant Steve Aitken said a section of a pine tree about 15m long which had probably been weakened by strong overnight winds split in two places, broke about 5m from the ground and fell on to the front passenger side of the car as it travelled up the hill.
The falling tree, which was about 50cm in diameter, pushed in the car's bonnet and smashed the windscreen before bouncing off the car and being wedged underneath.
The 38-year-old male driver had a suspected broken arm, while the 25-year-old female passenger suffered grazes and bruising from an air bag.
The child, who was safely secured in a back seat, was uninjured in the accident.
All three were transported to Dunedin Hospital by ambulance.
The car was extensively damaged and had to be towed away.
Council contractors removed the tree from the road.
Snr Sgt Aitken said if the tree had fallen slightly further back on to the car's roof, the passengers could have been seriously injured or killed.
"They were very, very lucky. They won't be winning Lotto this week - they have already had their share of good luck."
