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.
"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.
"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.
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."
