She exited from the front passenger seat, while a teenage boy who was driving, and three younger children, also got out of the Prado.
The mother is then seen hanging a blanket over the right rear window, followed by a jumper over the left side to hide the toddler from the view of passers-by.
The family then walk off together, leaving the child alone in the car.
Nine minutes later, the mother is seen on the footage returning to the car with the teenager to check on the girl.
Still asleep, they close the doors and remarkably leave her unattended again.
Three minutes later, a tow truck driver pulls up in front of the vehicle, peeps into the front window before taking a photo of the illegally parked car.
He then proceeds to put the vehicle onto the back of his truck, before driving away.
Another 20 minutes passes before the teenager returns with the three children to find the car gone.
The panicked mother reported the car stolen to police, who later spotted it on the back of the Nationwide Towing truck on Mt Alexander Rd in Ascot Vale.
The toddler only woke when police opened the car door and lifted the blankets covering her.
Police initially said they were not investigating the matter after the mother had told them she had made a quick pit stop to go to the toilet. But they today relaunched the investigation after the security footage came to light contradicting her story.
Witnesses have also told how the woman was dining in Fahita’s Restaurant when the car was towed.
“As the result of information received Fawkner Police will be conducting an investigation into what, if any, criminal offences have occurred following (the) incident,” police said in a statement.
Nationwide Towing operations manager Mark Beveridge says their driver was shocked to learn the child was inside the car.
“The driver was quite distraught, he couldn’t believe someone would leave their child asleep in the car unattended — he’s got children himself and was quite upset by the whole idea,” Mr Beveridge told AAP.
“We’ve been doing this for 20 years and this is the first time anything like this has happened.”
Mr Beveridge said the driver followed all procedures and was not at fault.
“I don’t really think the driver could have done any more to check the child was in there,” he said.
“He was very upset by it. He’s got children around the same age, and he was very distraught.”
Nationwide Towing has not issued a fine or towing costs to the mother.