The altercation is believed to have taken place on Monday in Oamaru, which she represents in Parliament, just days after Dean found her name dragged into an unrelated political stoush in Wellington.
"Jacqui has kept us informed and we have reiterated we are here to support her should she need anything at all," a spokesperson for National told The New Zealand Herald of the Oamaru incident.
"We expect to see Jacqui back in Parliament this week where she will continue to work hard on behalf of her Waitaki constituency."
The spokesperson declined to comment further on the case because it is before the courts.
The Herald contacted Dean this morning and she also declined to comment.
Police have confirmed that a woman has been summoned to appear at Oamaru District Court on December 15 regarding a charge of assaulting a person with a blunt instrument.
If convicted, the person could face up to five years' prison.
It is alleged the woman who was charged tried to hit the MP with her car following an argument relating to their dogs, according to Stuff. Dean was not hurt in the incident, Stuff reported.
On November 24, five days before the Oamaru incident, the politician inadvertently found herself in the spotlight after then-National leader Judith Collins cited Dean as a reason for demoting potential leadership challenger Simon Bridges.
Collins, who was ousted from party leadership soon after the move, said Bridges had shared crude comments with Dean during a function five years ago.
Bridges has previously apologised for his remarks, and did so again this week.
