Barba was scheduled to stage The Chronic Life, while Castellucci was to perform Julius Caesar at the festival.
They were also planning to hold workshops on the sidelines of the festival.
The organizers gave no reason for the postponement.
A number of Iranian artists have withdrawn from the Fajr festivals to express their sympathy with the families of those people killed following the unintentional downing of a Ukrainian plane by Iran.
The 38th Fajr International Theater Festival will take place in Tehran from January 30 to February 9.
Source: Tehran Times