Ferdinand was taken to hospital in South Africa for a scan after sustaining an injury to his left knee during a collision with Emile Heskey in the final moments of Friday's training session in Rustenburg.
Ruled out: Rio Ferdinand leaves hospital on crutches
He left Ferncrest Hospital on crutches before returning to England's training headquarters.
Tottenham defender Michael Dawson is on his way to South Africa having been called up as an emergency standby. He will now take Ferdinand's place in the 23-man squad.
Vice-captain Steven Gerrard will now wear the captain's armband in SouthAfrica.
Fabio Capello said: 'It is obviously bad news and everyone with the squad is very disappointed and sorry for Rio. It was an accidental injury in training, but had nothing to do with the pitch.'
Put through his paces: Rio Ferdinand taking part in England's first training session in South Africa
An England statement read: 'England captain Rio Ferdinand today suffered a left-knee ligament injury in training.
'Further to a scan arranged by the England medical staff immediately after training on Friday afternoon, Rio has been ruled out for four to six weeks and will therefore unfortunately miss the World Cup.
'Tottenham Hotspur's Michael Dawson has been contacted today and will fly to South Africa on Friday evening. Steven Gerrard will lead the England team as captain in the tournament.'
The huge blow comes just eight days before England's World Cup campaign kicks off against the United States.
Worry for England: Ferdinand is having a scan on his injured knee
LedleyKing and Jamie Carragher will both now fancy their chances of a placein England's defence for their World Cup opener on June 12.
Capelloearlier told reporters: 'The bad news is in the last moment of the training, Rio suffered a problem with the knee.
'He has just gone to hospital for a scan. We hope it will not be so bad an injury but we have Michael Dawson on call.
Reasons to be concerned: Ferdinand was dogged by injury problems last season with Manchester United
'It came from aminor tackle during the training. How bad is it? We will have to wait and see.'
Ferdinand had been optimistic of enjoying an injury-free World Cup after a season dogged by problems at Manchester United.
He made just 21 appearances for his club thisseason, starting only 13 Premier League games, in a season disrupted bya back injury.
However he had trained with no setbacks during England's two-weekcamp in Austria, and also came through the friendly internationals withMexico and Japan unscathed.
Training: Rio Ferdinand and Gareth Barry with the rest of the England squad in Rustenburg on Friday
Goalkeeper David James also missed training on Friday but Capello admitted to being much less concerned with that situation, insisting the39-year-old had'only a slight knee problem'.
England play their first World Cup match next weekend against the United States in Rustenburg on June 12.
They then face Algeria and Slovenia in their next two group games - on June 18 and June 23.
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