Zakharov died in Moscow on Saturday, according to the Lenkom Theatre, which he had led for more than four decades. The theater's chief administrator, Mark Varshaver, said Zakharov died of pneumonia.
Born in Moscow, Zakharov graduated from the capital's leading theater school in 1955 and worked as an actor for a decade before he became a stage director. He served as the Lenkom Theatre's director from 1973 until his death.
Many of Zakharov's theater productions become iconic. He also gained fame as a film director.
In a condolence letter, Russian President Vladimir Putin hailed Zakharov as a "colossal personality" and praised the late director's "remarkable talent, freedom and dignity."
Plans call for Zakharov to be buried Tuesday at Moscow's Novodevichy Cemetery.