The woman yelled at the girls, who responded by laughing.
She then got out of the car and attacked one girl, who suffered minor bruising to her face.
In a separate incident last Sunday, the same woman punched a woman on Carterton's High St.
The victim had just left New World supermarket and crossed the road to get an icecream from a van parked outside Carrington Park when the assault happened, Mr Day said.
The attacker was leaning on a white ute near the park and swore at the victim before pushing her and then punching her in the face.
Three men in their teens or early twenties were with the woman, but did not take part in the attack.
Mr Day said police believed it was likely the woman was still in the area. Unprovoked attacks such as this were "very rare" in Wairarapa, Mr Day said.
The Carterton victim, who did not wish to be named for fear of retaliation, was shocked by the random nature of the attack.
"I was in the wrong place at the wrong time ... I didn't expect anybody to attack me that suddenly."
In shock and with a profusely bleeding nose, she sought help from bystanders outside the supermarket who helped her in getting to the police station.
Her nose was not broken but was still bruised, she said.
She described the woman as "very angry" and "ready to start a fight with the next person who came by". She contacted the Times-Age in order to warn residents about the woman, she said.
"It's in our best interest if you know there's something to look out for."
"Maybe she will just back off because she will realise she can't just get away with it."
The attacker is described as Maori, in her early 20s, of average height and slim build with dark hair with blonde streaks at the front.
The white ute, registration DEF575, is a 1995 Nissan Navara registered to a Whangarei address, and may have a dog kennel on the back. Police advised the public not to approach the woman but call 111 or Crimestoppers.
