His latest setback came 15 minutes into Tuesday's 3-1 Premier League win over Bournemouth, which moved the Hammers up to fifth in the standings, ahead of Manchester United.
Carroll's injury means he will miss Saturday's game at relegation strugglers Newcastle United, as well as the visits of Manchester City and Aston Villa, and trips to Southampton and Norwich City.
He will also miss a fourth-round FA Cup tie against either Liverpool or Exeter on Jan.30.
Striker Nikica Jelavic will come into the side in Carroll's absence, with manager Slaven Bilic now unlikely to sanction a January move for the Croatian, who has made just one Premier League start this season.
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(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
