The star was due to join costars Cate Blanchett and Gael Garcia Bernal for Tuesday morning's screening of their movie Babel, directed by Alejandro González Iñárritu.
Instead, Pitt sent an e-mail that was read aloud at a press conference after the screening: "With the imminent arrival of the newest addition to our family, I am unable to join Alejandro, Cate, Gael and the rest of the cast and crew introducing the film."
He went on to say, "I am tremendously proud of Babel and want to congratulate everyone involved for this great achievement."
Babel's gala world premiere is scheduled to take place at the Cannes Palais du Festival on Tuesday night.
Pitt has been vacationing in Namibia with the pregnant Jolie and their kids Maddox, 4, and Zahara, 1.