The 33-year-old midfielder sustained the problem while taking a shot in the second half of his side's 4-1 win over West Ham in the Premier League on Saturday.
Gerrard underwent a scan on Monday and the results were made public on Thursday, with the club revealing that he will miss the remainder of 2013.
Liverpool manager Brendan Rodgers confirmed on the club's official website: "Steven is, as reported, probably going to be up to about four weeks or so.
"So he'll go through an extensive treatment programme over the next numbers of weeks and hopefully we can get him back that little bit sooner.
"But certainly at this stage, it was a four to six-week injury and we'll see how we look with that."
The England captain, who has started all 15 of Liverpool's Premier League games this term, will now miss the club's matches against Tottenham on Sunday, Cardiff City, Manchester City, Chelsea and Hull City.
It remains to be seen what part - if any - he will play in the FA Cup third-round clash against either Oldham Athletic or Mansfield Town at the start of January.
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