Fiorentina player Fernandez told reporters on Tuesday he had been carrying the problem for several weeks and surgery was now required to solve the issue, meaning he will be forced to sit out the tournament in Brazil next month.
Another Chile star, Arturo Vidal, underwent an operation on his knee earlier this month, but is expected to recover in time for his team's opening game against Australia on June 13.
"I'm not able to play the World Cup, I have to have an operation," Fernandez was quoted as saying by South American media.
"It was in my plans, I had only had discomfort and I thought it would not be serious.
"It was difficult as not playing at a World Cup is complicated. I was told it was serious.
"It would be irresponsible not to go one hundred percent to the World Cup. The ankle is not going to improve until my operation."
After their match against the Socceroos, Chile face holders Spain and 2010 finalists the Netherlands in Group B.
