Bennett Armistead Schauer was born Wednesday.
No other details regarding the baby's birth were immediately available.
Linney married Marc Schauer in May 2009.
She was nominated for a best actress Academy Award for ""You Can Count on Me" and "The Savages," and for a supporting actress Oscar for "Kinsey." Other film credits include "Hyde Park on the Hudson" and "Love Actually."
She won Emmy Awards for her work in "Wild Iris," "The Big C: Hereafter" and "John Adams," and for the comedy series "Frasier."
Other TV credits include the miniseries "Armistead Maupin's Tales of the City."