A representative for Morissette said in an e-mail on Monday that Ever Imre Morissette-Treadway was born Dec. 25. The statement said, "all are healthy and happy."
No other details were available.
The 36-year-old has won several Grammy awards, including album of the year for 1995's "Jagged Little Pill."
She also earned a Golden Globe nomination for best original motion picture song for "Wunderkind" from "The Chronicles of Narnia: The Lion, the Witch and the Wardrobe," and appeared as God in Kevin Smith's 1999 film "Dogma."
She had been previously been engaged to actor Ryan Reynolds.
The Associated Press contributed to this report.