Sturridge, who had to quit the England squad ahead of Friday???s Euro qualifier against Lithuania, suffered the injury against Manchester United last Sunday.
The 25-year-old, who has already missed a huge chunk of the season because of injury, is expected to sit out much of April including the trip to the Emirates on April 4 to face Arsenal.
England manager Roy Hodgson said: ???I???m disappointed for Daniel because he didn???t really feel that it was any problem.
“When he did the scan he was devastated as he didn???t want to leave. He has a slight tear and you can???t play through that.???