Gremio goalkeeper Marcelo Gorhe has also been called into the squad, replacing Benfica’s Ederson.
23-year-old Lucas Moura replaces Barcelona midfielder Rafinha, who has been forced to withdraw from the squad with a muscle injury after a week in the United States that saw him unable to train and miss his side’s Chevrolet Brasil Global Tour victory over Panama in Colorado on Sunday.
It was thought that Rafinha would be replaced by Palmeiras starlet Gabriel Jesus, who missed out on a call-up last week because he hadn't secured an American visa.
Kaka was instead asked to replace Bayern Munich’s Douglas Costa.
"The choice to call in Kaka was a technical decision," Dunga told the media on Saturday. "Unfortunately, other players could be here but they're not here because they did not have the required documentation."
Dunga has now been forced into four changes from his original 23-man squad, having also lost veteran Santos striker Ricardo Oliveira shortly before the team gathered in last week.
Benfica’s Jonas replaced Oliveira and celebrated his late arrival with Brazil’s opening goal in the 2-0 win over Panama.
Brazil begins its Copa America campaign on Sunday, June 4 against Ecuador.