Slimani is suspended from France's game in Wales on February 21 following confirmation of the punishment by the Six Nations disciplinary committee on Wednesday.
Rizzo, who was also shown a red card after the incident at the Stade de France, is out of Italy's home match against Scotland on February 22.
The flashpoint between Slimani and Rizzo, who had both come off the bench in the second half, occurred in the 72nd minute of France's 30-10 win.
"Both players agreed that the red cards had been correctly awarded by the referee," the Six Nations said, adding that both players were afforded a two-week reduction in their suspensions "in light of mitigating factors".
France are joint-top of the Six Nations table with Ireland, with four points from two games. Italy have lost their opening two matches.
(Reporting by Gregory Blachier; Editing by Stephen Wood)
