"He was investigated in 2006 for radicalisation, but (the probe) was not renewed in 2008. He had no criminal record," Cazeneuve said.
He identified the suspect as Yacine Salhi, 35, who was known to have lived around Lyon, France's second largest city, near the site of the attack.
"This individual has links with the Salafist movement, but had not been identified as having participated in activities of a terrorist nature," added the minister who rushed to the scene in eastern France.
Salafism is an extremist, puritanical form of the majority Sunni branch of Islam.
One person was killed and two injured during the attack in the small town of Saint-Quentin-Fallavier, around 40 kilometres from Lyon. A decapitated head was found pinned to the gates of the factory.
Cazeneuve said a local firefighter who rushed to the scene had overpowered and "neutralised" Salhi.
The minister said he had shown "courage and kept a cool head".
"I would like to offer my deepest thanks to the firefighter and his colleagues who came to the scene for their promptness and effectiveness."
Authorities were still working to identify the victim of the beheading, but he is believed to be a local businessman.
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