The driver of the car, a man in his 30s, became abusive and assaulted a Garda member at the scene.
She was was taken to Our Lady of Lourdes Hospital in Drogheda where she was treated for non-life threatening injuries.
The driver of the car was arrested and has since been charged and is due to appear before Dundalk District Court on the 6 January 2021.
Gardaà in Dundalk were also called to a public order incident at Coes Road around 9.20am on Tuesday morning.
During the course of the incident, a man aged in his 30s became abusive and assaulted a Garda member.