Prosecutors said there were no indications that the suspects had already chosen a specific target. They declined to give further information.
He is being investigated on terrorism, attempted murder and kidnapping charges, the source said.
The suspect appeared to have been planning to attack the Geoffroy Guichard stadium during the Olympic soccer tournament and was inspired by Islamist ideology.
AFP, citing a source, said the suspect had shouted out "Allahu Akbar" (God is Greatest) but Reuters could not confirm that.
"Antisemitism is not a threat only for French Jews. If antisemitism begins with the Jews, it never stops with the Jews," Yonathan Arfi, President of Crif said.