His injury has also caused huge concern for Chelsea coach Carlo Ancelotti as his side maintain their chase for the Premier League title.
The 29-year-old Chelsea left back suffered the injury in an accidental collision with Everton's on-loan United States striker Landon Donovan at Goodison Park on Wednesday.
The players were due to be on opposing sides when England face the U.S. in their opening World Cup match in South Africa on June 12.
"It is bad news about Ashley," Capello told reporters. "He's a really important player. As a left defender he is very good and dangerous going forward. I hope it won't be too tough for him."
Cole, with 77 caps, was Capello's automatic first choice on the left side of the defence, but the England coach could now be forced to call up understudy Wayne Bridge.
However, that situation is complicated because of the off-field problems surrounding Bridge and his former Chelsea team mate John Terry.
Terry was replaced as England captain last week following allegations in the British media that Terry had an extra-marital affair with the former girlfriend of Bridge, who joined Manchester City last year.
Roberto Mancini told a news conference on Friday it was important for Bridge to play for England.
"Ashley Cole's injury for England is a problem," said Mancini, "but we have a good player here in Wayne Bridge who can play for the national team.
"I think its important for him to play for England and if he is picked, he should play. Its very important for his career that if he can play in the World Cup, he should play."
Capello does have other options for the position including Aston Villa's Stephen Warnock or James Milner, Leighton Baines of Everton or Gareth Barry and Joleon Lescott of Manchester City.
Cole is in a race against time to be fit for the World Cup. The Premier League season ends on May 9, with the FA Cup final on May 15 and the Champions League final on May 22.
England also have a World Cup warm-up game against Mexico on May 24 and a planned friendly with Japan in late May in Austria before Capello names his World Cup squad on June 1.
Chelsea coach Ancelotti must also decide on who will replace Cole as his team maintain their push for the league title.
Ancelotti can call up Yuri Zhirkov or Paulo Ferreira, but told reporters on Thursday: "We are very disappointed because he is a very important player. Now we have to do our best to get him recovered quickly."
