The French soldier was on a group patrol as part of a national protection program when he was attacked from behind, prosecutor Robert Gelli told Europe 1 radio. The assailant did not say a word, Gelli said.
"There are elements the sudden violence of the attack that could lead one to believe there might be a comparison with what happened in London," Interior Minister Manuel Valls told France 2 television. "But at this point, honestly, let us be prudent."
Rigby was attacked while walking outside the Royal Artillery Barracks in the Woolwich area of south London.
The gruesome scene was recorded on witnesses' cellphones, and a video emerged in which one of the two suspects his hands bloodied boasted of their exploits and warned of more violence as the soldier lay on the ground. Holding bloody knives and a meat cleaver, the suspects waited for police, who shot them in the legs, witnesses said.
In the video, one of the suspects declared, "We swear by almighty Allah we will never stop fighting you ... We must fight them as they fight us."
Two Muslim hard-liners have identified that suspect as Michael Adebolajo, a Christian who converted to Islam and attended several London demonstrations organized by banned British radical group al-Muhajiroun.
French security forces have been on heightened alert since their country launched a military intervention in the African nation of Mali in January to regain territory seized by Islamic radicals. British Prime Minister David Cameron was himself in Paris meeting with Hollande when he first received word of the London attack.
Last year, three French paratroopers were killed by a man police described as a French-born Islamic extremist who then went on to strike a Jewish school in the south of France, killing four more people.