Her fiance, bass-baritone Erwin Schrott, attended the birth. The name of the child wasn't announced.
"Both parents are delighted that their son has finally arrived and look forward to introducing him to family and friends in the coming days," said her manager, Jeffrey Vanderveen.
Netrebko, who turns 37 on Sept. 18, last performed June 27 at a concert in Vienna. She is scheduled to return to the stage Jan. 14 and 17 in the title role of Donizetti's "Lucia di Lammermoor" at the Mariinsky Theater in St. Petersburg, Russia, then perform the same role at New York's Metropolitan Opera starting Jan. 26.