The Argentine-born film-maker died in hospital in Sao Paulo on 13 July after a heart attack, Denise Winther of Babenco's HB Films said.
Kiss of the Spider Woman, a surreal prison drama, was also nominated for best picture at the Oscars, while William Hurt won best actor.
Babenco also directed 1987's Ironweed with Jack Nicholson and Meryl Streep.
Both Nicholson and Streep were nominated for best actor and actress Oscars in the film about an alcoholic drifter.
Babenco's most recent film was last year's My Hindu Friend, a film about a film director very close to death, starring Willem Dafoe.
Babenco leaves his wife Barbara and daughter Janka.
Hector Babenco, the Brazilian director nominated for an Oscar for 1985's Kiss of the Spider Woman, has died aged 70.