He said police acted in a "militarised and aggressive manner" in detaining him and nearly 200 other people last month.
The protests were against the killing of Alton Sterling, a black man, in the Louisiana city.
State governor John Bel Edwards has previously said the police's response was appropriate.
Mr McKesson was held on 9 July on a charge of obstructing a highway.
In the lawsuit, he and two other fellow protesters claimed that police were unnecessarily aggressive during the arrests.
It said that "defendants used excessive force in attacking, battering, beating and assaulting plaintiffs and class members without provocation or the need for defence".
The three arrested protesters said they wanted the lawsuit to have class action status.
The shooting of Alton Sterling was one of a string of police killings of black people by white police officers in recent years that triggered mass protests and rekindled debates about race relations in the US.
Black Lives Matter activist DeRay Mckesson is suing the police and city of Baton Rouge over mass arrests during protests against police killings.