The 29-year-old, who has made more than a century of league appearances for the Premier League leaders since arriving from Arsenal in 2006, picked up the injury following a challenge by USA international Landon Donovan during the Blues' 2-1 defeat to Everton at Goodison Park on Wednesday.
The injury is expected to keep the highly-rated left-back out until the end of the season, and he now faces a race against time to be fit in time for the World Cup finals in South Africa, which begins in June.
Cole's injury increases the likelihood that Manchester City full-back Wayne Bridge will start England's upcoming international against Egypt alongside Chelsea captain John Terry.
Asked if he would be fit for the World Cup, Chelsea manager Carlo Ancelotti told Sky Sports News: "I think so. I hope so for him and the for the England team."
Chelsea will be without Cole for their Champions League last 16 first-leg tie at Inter Milan on February 24 and the second leg on March 16 when the club's former manager Jose Mourinho returns.
"Now we have to do our best to help him recover quickly (but) Yuri Zhirkov is a fantastic full-back so we can use him," he said referring to the Russia midfielder who usually plays in an attacking role but can also fill in at left back.
