"This extremely grave barbaric action is also an attack against democracy and the freedom of the press," the French Muslim Council (CFCM) said in a statement.
The body represents France's Muslim community, which is Europe's biggest and estimated to number between 3.5 million and five million people.
The two or three heavily armed gunmen who stormed the offices of the Charlie Hebdo weekly, the focus of several attacks since publishing cartoons of the prophet Mohammed in the mid-2000s, shouted Islamist slogans as they fired.
The Muslim council also called for calm and urged Muslims to beware of extremist manipulation.
"In this tense international climate stoked by the madness of terrorist groups unjustly claiming to represent Islam, we call on all those attached to the republic's values and to democracy to avoid provocation", it said.
The Muslim community must practise "the greatest vigilance towards possible manipulation by extremist groups," it added.
A separate statement from an organisation close to the Muslim Brotherhood, the Union of French Islamic Organisations (UOIF), also condemned "in the firmest manner this criminal attack and these horrible murders."
France also has Europe's biggest Jewish population of between 500,000 to 600,000.
