"We have spoken to (coach) Dunga....and we've decided that, because he is still not in his best form and because he is still feeling some pain, he will stay in Brazil," Runco told reporters at the team's training camp in Teresopolis.
"We are dealing with a national team player, of the highest level, who has been lent to us by another institution and you have to respect this and send him back in good shape.
"We would not create any type of situation which could damage the health of the athlete."
The AC Milan player has been struggling with the injury since February and had been given a 50 percent chance of playing.
Runco said that Kaka would fly straight to Porto Alegre where Brazil host Peru in another qualifier on Wednesday.
"He will continue the physiotherapy and wait for us to return from the game against Ecuador," Runco said.
"We have two concerns which are that he corrects the way he walks, which has been modified since he suffered the injury, and he recovers hit fitness."
Dunga said nobody would be forced to break the pain barrier to play for his country.
"Nobody sacrifices themselves here with the Brazil team," he said. "Our spirit is that the player has to be in perfect condition to play.
"We've decided that he will stay in Brazil and avoid this tiring journey."
Brazil are second in the 10-team South American group with 17 points from 10 games, six behind leaders Paraguay.
The match in Quito, where Brazil have lost 1-0 on their last two visits, will be played at 2,800 metres above sea level.
