Frederiksen, who was at the court to meet a commission into her government’s decision last year to cull fur farm mink, was not in the car at the time of the incident.
Demonstrators surrounded the car when it began to move, resulting in police deciding to shield it.
Copenhagen Police told news wire Ritzau that “in connection with the car being moved, it was encircled by demonstrators”.
“In connection with this, a rear light was smashed on the car. It has now been driven away from the location. We are looking further into what happened,” police added.
Two people were arrested as a result of disturbances related to the demonstrations, Copenhagen Police confirmed to Ritzau later on Thursday.
One of the individuals was arrested for breaching laws against violent or threatening behaviour towards service personnel such as police officers, and the other for making offensive remarks.
Frederiksen met a sizeable gathering of demonstrators when she arrived at the court building in Frederiksberg shortly before 9am on Thursday.
One sign held by protestors called for her to be put in prison while also referring to text messages relating to the mink decision that were automatically deleted from the prime minister’s telephone.
Another sign read “Ignorance does not relieve you of responsibility”, referring to the fact the government has argued it did not know the order to cull mink had no legal basis at the time it was issued.
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Frederiksen defended the decision to cull the minks on Thursday as she arrived at the court building.
“I think, generally speaking, that we unfortunately had to make a decision one year ago to cull all mink. It was the right decision. I will now go in and answer the questions that are asked,” she said.