The police were said to have fired their guns at the vehicle after routinely stopping the driver for speeding.
A high-speed chase then reportedly ensued, and the shots were fired. Five children were said to have been traveling in the vehicle at the time.
Sky reports that the shooting followed a 'bizarre incident' which has also left the driver, 39-year-old mum, Oriana Ferrell, and her 14-year-old son facing charges.
Ferrell was stopped by a New Mexico state police officer for driving at 71mph in a 55mph zone near Talpa, on October 28. A patrol car's video footage captured her arguing with the officer before driving away.
She was pulled over again, and a police officer tried to pull her out of the car when she refused to get out.
One of the children in the car got out and confronted the officer, but got back in when the officer pulled out his taser.
Ms Ferrell then drove off at speed, resulting in another officer allegedly firing three shots into the back of the minivan. The vehicle was stopped again 10 minutes later and Ms Ferrell was arrested.
ABC News reports she was charged with five counts of abuse of a child, aggravated fleeing from an officer, resisting arrest, reckless driving and possession of drug paraphernalia, while her teenage son was charged with battery of an officer.
But the officers' actions are now also under scrutiny via an internal investigation.
New Mexico state police chief Pete Kassetas told ABC the incident was 'an intense, 43-minute-long, dangerous situation that placed the public at risk'.
"I have, of course, reviewed the video and do have concerns relating to the conduct of the officer who discharged his firearm," he said.
Ms Ferrell's lawyer said there had been 'no reason at all to chase her down'.