The blast was the sixth of a series of bombings or attempted bombings in France since late July, and the first car bomb on the French mainland since 1982.
Police said they had detained for questioning a man seen with two others just before the attack in the city, about 270 miles from Paris.
Among the injured were three children, who suffered smoke inhalation. Three other children suffered shock.
Lyons's deputy head rabbi, Isaac Elhadad, said a faulty school clock had delayed the children's exit by two minutes and saved dozens of lives.
"We can thank God that this attack did not cause total carnage, because it happened at exactly the moment school gets out," he said.
The blast destroyed the car, a locally registered Opel, set fire to another parked near by and ignited a blaze in an adjacent apartment, officials said.
The explosion occurred at 4:55pm as classes ended at the school of about 700 students and parents waited to pick up their children.
The blast came three days after a bomb was found in Paris and defused. Three bombings in Paris since July have left seven people dead and more than 100 injured and have prompted heavy security measures.
Algerian Muslim fundamentalist extremists, who have threatened France for its support of the Algerian military-backed government, are prime suspects in the attacks.
Police have mounted a nationwide effort to tighten security and search for suspects since the first bombing in a Paris subway train on 25 July killed seven people and injured 84. Another bomb wounded 17 people near the Arc de Triomphe on 17 August; and on 26 August a bomb was found on a high-speed train track north of Lyons. The bomb, made from a gas canister filled with explosive and bolts, failed to go off.
Investigators believe the three bombs were planted by the Armed Islamic Group, which is seeking to topple the Algerian government and establish an Islamic state.
t Brussels - The French barrister Jacques Verges blamed an Algerian special military unit for recent bomb attacks in France. Proof, he said, would be supplied soon, Reuter reports.
"I accuse the Algerian special services of being responsible for these attacks," he told a Brussels court in his defence plea for a suspected Algerian fundamentalist leader, Ahmed Zaoui, who is being tried for allegedly possession of explosives. Mr Zaoui, believed to be second-in-command in Algeria's most feared fundamentalist movement, the Armed Islamic Group (GIA), and 12 other defendants deny membership of the organisation.