The driver slows down, before nudging the protesters with the bonnet. A policeman then clears the protesters out of the way and the car drives away.
Mr Borrows defended his actions, saying he did not believe he had struck any of the protesters.
"I was inching forward, they were taken out of the road, and I didn't drive until the road was clear.
"I had no idea that anything had happened and I am pleased to see that the woman doesn't have any broken bones or anything like that."
He added: "Everyone's got a right to protest, I don't have an issue with that at all. I'm just pleased that the lady is not hurt."
The MP said he later saw a post about the incident on Facebook, after which he called the police.
They had not contacted him again yet, but he expected to hear from him.
"I am quite happy to talk to the police and to tell them what happened," he said.
Social Housing Minister Paula Bennett was also in Mr Borrows' car at the time.
The injured woman, Tracy Treadwell, was taken to Whanganui Hospital.
Ms Treadwell is recovering at home and has been told by police the matter will be thoroughly investigated..
"My foot is still sore but my knee that was twisted when the car went over my foot is more painful," Ms Treadwell said.
"I have been interviewed by a police detective who advised me that there will be a thorough investigation and it could be a lengthy process."
Whanganui TPPA Action Group protester Denise Lockett told the Whanganui Chronicle that Ms Treadwell's foot was badly bruised.
She also alleged that her own ankle was hit by Mr Borrows' car. She was disappointed the MP did not allow time for the activists to move out of the way.
"The police were standing behind us and Tracy didn't have room to step back because there was a police officer behind her," she said.
In a post on Facebook, Ms Lockett said she had made a statement to police about the incident, which occurred outside the Collegiate Motor Inn in Whanganui.
"This was an extremely serious event, an MP driving his car into a group of women is just not acceptable."
She thanked the police officer at the scene, "who pulled me away as my leg was caught under the car and I was unable to escape as Chester just kept on driving".
A woman, who said she was Ms Treadwell's daughter, posted a picture of her on Twitter in an ambulance stretcher.
She sent the picture to Mr Borrows with the caption: "Anything to say?"
An MP must leave Parliament if they are convicted of a crime which has a maximum penalty of two or more years' jail.
Lawyer Graeme Edgeler said that careless or reckless driving on its own was not a particularly serious offence.
"If someone was injured, then it becomes much more serious," he said.
"He was driving quite slowly. But if [police] are looking at it, and the person was injured, then the appropriate sentence would probably be careless driving or reckless driving causing injury."
The maximum penalty for careless driving causing injury is three months' jail or a fine of up to $4500.
The maximum rises to five years' jail or a $10,000 fine for dangerous driving resulting in an injury.
Before entering Parliament, Mr Borrows worked as a police officer and a lawyer. He became an MP in 2005.
