The American Civil Liberties Union of Louisiana announced the lawsuit Wednesday.
The groups allege that authorities used excessive force, carried out mass arrests and verbally and physically abused protesters.
The lawsuit describes the protests as peaceful and blames law enforcement for escalating the situation.
The shooting death last week of Alton Sterling at the hands of two white police officers sparked outrage among many in the black community.
The police have come under fire for tactics they used on protesters over the weekend. Over a three-day period, police arrested about 200 people.
The governor has defended the police, calling their response "moderate."EARLIER REPORT:
An attorney for relatives of a black man who was fatally shot during a struggle with two white Baton Rouge police officers is urging Louisiana's attorney general to "fight for justice" in the case.
The lawyer, Justin Bamberg, told reporters Wednesday that Alton Sterling's family is pleased that the Justice Department is investigating the July 5 shooting but said that's not enough. Bamberg said the family wants an indictment in the case and hopes state Attorney General Jeff Landry's office "one day" will get involved.
In a statement Monday, Landry said he won't have access to details of the federal investigation of Sterling's shooting until it's completed and a decision has been made on potential federal charges.
Bamberg compared Sterling's shooting to the fatal shooting of a 6-year-old boy last year by two deputy city marshals in Marksville, Louisiana.
Bamberg noted that Landry's predecessor obtained indictments in December against the two black deputies on second-degree murder charges in the death of Jeremy Mardis, who was white.EARLIER REPORT:
The teenage son of a black man killed by white police officers is speaking out for the first time, telling reporters gathered at the Triple S convenience store where his father died that he wants everyone "to protest the right way, protest in peace."
Cameron Sterling spoke to the crowd in Baton Rouge on Wednesday calling his father, Alton Sterling, "a good man," adding "and he will always be a good man."
The 15-year-old, who a week ago had sobbed as his mother, Quinyetta McMillon, talked about Sterling's death, stood composed as he called for peace, saying he wanted protesters angry about his father's death to "protest in peace."
He said there should be no violence.