"It's highly dangerous," Dr Galtry said. "I'm all for breastfeeding but not while driving a car."
Dr Galtry said mothers could not have babies dangling in mid-air while breastfeeding.
"You have to be holding some part of the baby."
She advised frustrated mothers with screaming babies to pull over and stop the car in a safe place before breastfeeding.
Dr Galtry said it was also dangerous for passengers in a moving vehicle to breastfeed. "If you're sitting in the passenger seat and you've got a screaming baby, I can imagine the temptation, but I mean, really."
Sergeant John Fagan told Newstalk ZB police knew the woman's car registration number.
In 2009, a woman in Ohio, United States, faced charges of child endangerment after breastfeeding her baby and talking on her cellphone while driving.