The 21-year-old singer-songwriter is expecting a baby in early August with her husband, Teddy Landau, the magazine said. The couple were married last May. Landau, 40, is Branch's bass player.
A call to her agent by The Associated Press wasn't immediately returned Friday.
Branch and Landau are scheduled to begin a 23-city tour next week featuring contributors to the soundtrack of the WB's "One Tree Hill."