Sam Allardyce confirmed the news prior to West Ham's Premier League meeting with Chelsea on Saturday lunchtime, indicating to Sky Sports that the injury was "pretty severe".
Carroll, 23, signed for the Hammers from Liverpool on a season-long loan in the summer.
Sam Allardyce: "We weren't expecting it to be as severe as it is.
"We now expect him to be out for six to eight weeks.
"It is a blow for us and for Andy of course. There is not a lot you can do about trauma injuries."