The Brazilian center back will require surgery, the Premier League club said Monday, and then will begin a rehab program.
Villa did not say how long it expects Carlos to be sidelined.
The 29-year-old Carlos joined Villa from Sevilla during the offseason and started the team's first two games in the Premier League, a loss to Bournemouth and the 2-1 win over Everton on Saturday.
He sustained the injury in second-half stoppage time against Everton.
Carlos was part of the Brazil squad that won gold at the Tokyo Olympics last year.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)