Manager Roy Hodgson, already without injured captain Steven Gerrard, said at the weekend that the player would be out for several weeks.
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The 32-year-old former England centre-back, who was injured in Sunday's 2-1 defeat to Tottenham Hotspur at White Hart Lane, told the Liverpool website of his disappointment after a scan.
"I'll be having surgery at the end of the week," said Carragher, who was making his 450th appearance in the Premier League.
"The average (time out) is about 12 weeks. I'd like to come back before that but I've got to make sure it's right. It will probably be late February or early March when I'm looking to come back."
"It's difficult for me when I'm injured. It hasn't happened very often, and I'm very lucky with that I suppose, but maybe it's caught up with me a little bit now.
"I've been here before with a broken leg which put me out this length of time. It's not easy but you've got to get on with it and it makes you more determined to get back.
"I'm sure towards the end of the season when people are maybe feeling a little bit tired I'll be raring to go."
