The Poland international suffered the problem during his side's 3-1 defeat at Stamford Bridge on Sunday and adds to the Saints' growing injury list, which includes Morgan Schneiderlin, Guly do Prado and Kelvin Davis.
With keepers Boruc and Davis both on the sidelines, Pochettino is set to hand 21-year-old Paulo Gazzaniga his first Premier League start since December 2012 against Aston Villa on Wednesday.
|9/2||Aston Villa are 9/2 with PaddyPower to score two goals against Southampton|
Southampton go into the clash with Paul Lambert's men on the back of successive league defeats at Arsenal and Chelsea but Pochettino insists that he is looking forward rather than back.
"We don't have time to dwell on our two consecutive defeats because we're only thinking about [Wednesday's] game," he stated.
"We've lost on two very difficult grounds at Arsenal and Chelsea. Now we'll try to impose our values and get the win.
"I'm expecting a physical game. Aston Villa are a strong side and very good on the counterattack, especially away from home. We're fully aware that they are a very dangerous side, so it'll be a very tough game."