Ferdinand suffered the injury in training yesterday morning and was sent straight to the local Netcare Fearncrest Hospital for a scan.
Both doctors travelling with the England team assessed the severity of the problem and came to the same conclusion – the Manchester United man would play no part in the competition.
"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," said a statement.
"Tottenham Hotspur's Michael Dawson has been contacted (yesterday) and will fly to South Africa.
"Steven Gerrard will lead the England team as captain in the
It is a grievous blow for coach Fabio Capello, who rated Ferdinand as one of the most influential players in his squad as well as a lynchpin in his defence.
He must now decide who to replace Ferdinand with, having added Dawson to a list of central defenders that also includes Ledley King, Matthew Upson and Jamie Carragher.
"It is obviously bad news and everyone with the squad is very disappointed and sorry for Rio," said Capello.
"It was an accidental injury in training, but had nothing to do with the pitch."
Manchester United will decide whether the injury was in any way related to the long-standing back problems that condemned Ferdinand to spend so much of this season on the sidelines.
Latterly, he missed a couple of games with a groin problem picked up during a match at Blackburn, although he has spent the past two weeks insisting he was over all his fitness issues.
Ferdinand had also opted not to speak too extensively about having the chance to emulate another former West Ham player, Bobby Moore, by lifting the World Cup.
"I have always said I would not let myself get too emotionally involved with situations and scenarios for fear that it might not happen or I might not achieve the goals I set out to achieve," he said during England's recent altitude training camp in Austria.
"I am not letting myself think what it would be like to be captain at the World Cup or lift the trophy. Maybe it is just superstition."
Those concerns have now come true, which must have an adverse effect on England's chances of landing the biggest prize in the game in Johannesburg on July 11.
Upson has started nine of the last 17 internationals while King has forced his way into Capello's thinking despite his long-term knee problem.
King has impressed for Tottenham this season and did train yesterday morning. By his own admission he looked far from convincing in the recent friendly with Mexico at Wembley, but he would be the current favourite to partner John Terry in the Group C opener against the United States in Rustenburg a week today.
Capello has pencilled Carragher in as the back-up right-back to Anfield team-mate Glen Johnson, while Dawson was named in Capello's initial party of 30 for the finals but was excluded from the final 23 after not playing against either Mexico at Wembley or Japan in Graz.
He has had an outstanding season at Tottenham, often alongside King, although he is yet to make his bow at senior international level and – while he was talking in relation to Adam Johnson – Capello has already spoken of the difficulty uncapped players have in stepping up to international level at such an important time.
Having to wrestle with such problems was surely not what was going through Capello's mind a few hours earlier when he spoke to David Cameron and accepted the Prime Minister's best wishes.