"Mario Gavranovic badly injured his knee in Switzerland's training in Porto Seguro on Saturday," said the ASF statement.
The FC Zurich forward's foot got stuck in the turf when he fell badly.
A scan revealed he had torn his cruciate ligament. He will now go back to Switzerland for an operation.
The 24-year-old, who has 11 caps, is unlikely to play again in 2014, the ASF said.
Switzerland play in the last 16 clash against Lionel Messi's Argentina in Sao Paulo on Tuesday.