The 29-year-old picked up the injury while warming up for Sevilla's game at Almeria on Saturday and while his absence will be a big blow for his club he said fans of Brazil need not worry about his fitness.
"I'm relaxed, and Brazilian fans can also stay calm because I'll be 100 percent at the World Cup," he said in a statement.
Fabiano is a key figure in Brazil's plans for South Africa, and although he was making a good recovery, they demanded he was released to join up with the rest of Dunga's squad, Sevilla said on their website.
Sevilla will also be without Spain striker Alvaro Negredo, who was sent off during the 3-2 victory over Almeria for protesting a decision.
Negredo's third straight red card of the season will not have done his chances of making Vicente del Bosque's final 23-man squad for South Africa any good.
Both Atletico and Sevilla have had to request permission for World Cup-bound players to be released for the Cup final at the Nou Camp, because of the date chosen by the Spanish football federation for the event.
National teams take priority this week, unless a side is playing in the Champions League final, and Atletico have also been sweating over the availability of some of their top players.
Argentina have given permission for striker Sergio Aguero to play, but Atletico are still awaiting confirmation from Portugal with regards to midfielders Simao and Tiago, and from Uruguay for top scorer Diego Forlan, the club said in a statement.
All three have been included in Quique Sanchez Flores's squad.
After undergoing treatment on his injury, Fabiano will join the Brazil squad in Curitiba on Friday.
"I will have intensive treatment in the coming days and I'm sure I'll be fine for the Brazilian national team on Friday," he said.
"I'm disappointed...but I'm going with a clear conscience because I gave my best for the club this season and just did not go to the game because it was vetoed by the medical department."
