The 31-year-old suffered a knee ligament injury in England's first training session in Rustenburg and was ruled out for up to six weeks following a scan.
It follows an injury-blighted season in which he was restricted to just 13 Premier League games for Manchester United with a debilitating back problem.
Zahavi revealed the central defender's devastation but backed Ferdinand to lead England in the 2014 World Cup.
Zahavi told The Sun: "Rio said: 'I think somebody cursed me.' That is honestly how he feels.
"Rio is very down. He cannot understand why this has happened to him."
Zahavi added: "This injury is nothing to do with the ones he had before.
"It is completely different and it is very bad luck.
"Rio was feeling sharp and was ready for the World Cup.
"He has waited so long for this tournament and to try and help England win it. He had prepared himself so well.
"But he is a very strong man and he will be back.
"I'm sure he will be leading England in four years time at the next World Cup."
Fabio Capello, meanwhile has admitted there was an immediate sense of shock when Ferdinand suffered the injury.
"It was a tackle and then there was big pain," said the Italian.
"He put his feet in the grass with Heskey and then he moved.
"The other players were upset. They stopped training.
"All the players who are here with me are important. But he is one of the starting players, the captain, a leader."
Scan results were assessed by two different members of the England medical team, but agreement was instant; Ferdinand has been ruled out for up to six weeks, which offered no opportunity for recovery in time to play any part in South Africa.
"It couldn't have been much worse on my first day," Capello admitted.
"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.
"It is the curse of the captain."
Ferdinand's injury leaves Capello with a tricky selection dilemma.
Matthew Upson has tended to stand in for Ferdinand during his many injury absences. His appearance alongside Terry for the March friendly against Egypt at Wembley - when Gerrard captained his country as he will now do for the World Cup - was his ninth start in 17 internationals.
The alternatives are Jamie Carragher, who was persuaded to abandon his international retirement by Capello this spring, and Ledley King - who for all his well-chronicled knee problems actually made twice as many Premier League appearances for Tottenham this term as Ferdinand managed for Manchester United.
King would be regarded as the early favourite, even though he did look rusty in the recent friendly against Mexico. He was able to get his name on the scoresheet and his form in the latter weeks of the season for Spurs belied the fact he does not train with any great regularity.
"You have to take into account this might happen: sometimes it happens during a game, sometimes in training, sometimes before you get to a final," shrugged Capello.
"You have to deal with it."