The Algerian Democratic Rally for Peace and Progress (RDAP) and its offshoot the United Arab Organisation (OAU), which both state that their goal is "the defence and support of Muslim and/or Arab people", are seeking damages of 580,000 euros ($750,000).
Their suit targets the publication, its director and two cartoonists.
Two other groups have already filed suits against Charlie Hebdo over the same series of cartoons. The most recent suits say they besmirched the honour of the prophet and of Muslims.
"Yet again, they are trying to scare us to prevent us continuing this French humoristic tradition regarding religion," said the weekly's lawyer Richard Malka.
In 2008, the then-director of Charlie Hebdo, Philippe Val, was cleared after French Muslim groups took him to court accusing him of having insulted Islam by publishing cartoons of the prophet.
An appeals court in Paris ruled that he had not insulted Muslims because the cartoons were aimed clearly at Islamist extremists and not the Muslim community as a whole.
In November 2011 Charlie Hebdo caused further offence when it published an edition "guest-edited" by the Prophet Mohammed that it called Sharia (Islamic law) Hebdo. The magazine's offices in Paris were subsequently fire-bombed.