She said she was not using her cellphone at the time of the crash.
The crash happened at 12.30pm on October 11 while Luxton was travelling on State Highway 1 at Winchester, north of Timaru.
Luxton said she was not injured in the incident.
"After checking that the occupants were unharmed I returned to my car and retrieved by phone from my purse to call the police," she said
"I gave my statement to Police and to date no further action has been taken."
She said at this stage no further action had been taken.
A police spokesperson said the crash was still under investigation.
Luxton is a second-term Labour MP. She entered Parliament as a list MP in 2017 and in 2020 she won the Rangitata electorate. The seat spans the areas of Timaru, Temuka and Ashburton.