The Union of French Islamic Organisations (UOIF) issued the fatwa condemning the disorder and destruction the unrest has caused.
Interior Minister Nicolas Sarkozy and other officials have been hinting that some Muslim groups may be involved in inciting angry teenagers to defy the French state.
Muslim residents, who are also affected by the unrest in the poorer, neglected suburbs, say rioters' anger is more about unemployment and discrimination than religion.
France's 5 million Muslims make up almost 8% of the population and say they are being treated as second-class citizens.
Reuters quoted the fatwa as saying: "It is formally forbidden to any Muslim seeking divine grace and satisfaction to participate in any action that blindly hits private or public property or could constitute an attack on someone's life.
"Contributing to such exactions is an illicit act," declared the decree, which said it was applicable to "any Muslim living in France, whether a citizen or a guest of France".
Call for calm
Prime Minister Dominique de Villepin received Dalil Boubakeur, head of France's Muslim Council, and imam of the Grand Mosque of Paris on Saturday.
A group of residents were forced
to seek shelter in the suburbs
But many influential local Muslim organisations in suburbs such as those experiencing daily unrest are closer to the UOIF than other national Muslim groups.
Many imams and other local organisations in the suburbs have called for calm.
Muslims were angered last week when police fired a teargas canister into a mosque, forcing worshippers to abandon prayers and disperse.
Boubakeur said after meeting Villepin that Sarkozy and other officials should be using words of peace, adding: "In such difficult circumstances, each word is important."
Sarkozy inflamed violence
The violence began last week when two teenagers, of African and Arab origins, were electrocuted while hiding in an electrical sub-station after fleeing a police identity check.
Sarkozy, accused of inflaming violence with tough talk and calling troublemakers "scum" - visited the hard-hit Essonne region early on Sunday to "give police support," he said.
The decree condemns violence
and destruction of property
Muslim leaders criticised him for his choice of language just before the rioting when he called delinquents "rabble" and vowed to clean their districts "with a power-hose".
"It was calm for a long time here. If there hadn't been Sarko's words - power-hose, rabble - there wouldn't have been all this," a 22-year-old man in the northern tinderbox suburb of Aulnay-sous-Bois was quoted by AFP as saying.
"He makes us suffer; he's a racist. He's put fuel on the fire," Fatou, a 14-year-old boy of African background, said.
Sarkozy has been preparing a bid to run in 2007 presidential elections on the strength of "zero tolerance" law-and-order policies.
French government acknowledgment
The government acknowledged that the grim conditions in the suburbs - chronic high unemployment, racial discrimination, miserable housing, drugs - had much to do with the discontent.
The riots have spread from Paris's bleak suburbs to other French cities. Towns such as Toulouse, Nantes and Strasbourg were hit by violence on Sunday.
Speaking from Paris, Michele al-Kik, Aljazeera's bureau chief in France, said police have installed closed-circuit cameras in and around the city of Paris in a bid to curb the unrest and assist in arresting rioters.
But the move has not deterred rioters and it seems the unrest has intensified despite the crackdown by French police.