The 21-year-old suffered the injury during France's under-21 win over Northern Ireland on Thursday.
A club statement read: "Aston Villa can confirm defender Jordan Amavi has been ruled out for the rest of the 2015-16 Premier League season with a ruptured anterior cruciate ligament in his right knee."
"Everyone at the club wishes Jordan a speedy recovery and we look forward to seeing him back on a football pitch as soon as possible."