Teenage fly-half Jalibert limped off in the first half of Les Bleus' 15-13 opening-day loss at Stade de France after being handed a debut by Jacques Brunel.
Jalibert sustained a partial tear to his posterior cruciate ligament and faces a lengthy absence, bringing his first professional campaign to a premature end.
Lionel Beauxis has been called up as a replacement and could win his first cap in six years against Scotland at Murrayfield.
Scrum-half Dupont suffered a torn anterior cruciate ligament that will keep him out of action until next season, while back-row Kevin Gourdon will be missing for around three weeks due to an ankle injury.
France head coach Brunel has also added the uncapped Baptiste Couilloud and number eight Louis Picamoles to his depleted squad.