The Orlando City midfielder, 34, will replace Bayern Munich's Douglas Costa, who was removed from the squad because of an injury to his left thigh.
Ex-AC Milan and Real Madrid player Kaka has been a regular in coach Dunga's squads, without getting much game time.
He has won 91 caps and scored 29 goals, but has only played 60 minutes for his country in three years.
Kaka is the second player to be added to the squad because of injury, with Benfica's Jonas replacing Santos striker Ricardo Oliveira.
Brazil have been drawn in Group B with Ecuador, Haiti and Peru for the tournament, which is staging a special 100th anniversary edition.
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The German-based team, which won Le Mans 13 times between 2000 and 2014, finished third in 2015 and 2016, with both races won by Porsche.
Formula E, the world's first electric racing series, only started in 2014.
Audi chairman Rupert Stadler said: "We're going to contest the race for the future on electric power."
Ten teams - including Renault, Audi and Jaguar - currently take part in the Formula E series, with two new entries to be allocated for 2018-19 subject to the approval of the International Automobile Federation (FIA).
Formula 1 champions Mercedes are considering taking an option to join.
"As our production cars are becoming increasingly electric, our motorsport cars, as Audi's technological spearheads, have to be even more so," Stadler added.
Pierre Fillon, president of the Automobile Club de l'Ouest, which organises the Le Mans race, said: "It was with emotion that we all learned this morning about Audi's decision to withdraw from endurance racing.
"Although prepared for this, we regret the departure of a major figure in endurance racing for a different adventure."
Kaka has been called up to the Brazil squad for next month's Copa America in the United States.
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Audi will not race in next season's World Endurance Championship, which includes the iconic Le Mans 24 Hours race, to concentrate on Formula E.