The couple have twin daughters, Eva and Katie, born in 2004.
"Martie is doing very well and Gareth and the family are over the moon," the band said in a statement.
Maguire, 38, plays fiddle and mandolin in the Dixie Chicks, which also includes Natalie Maines and Maguire's sister, Emily Robison. Hits by the Chicks include "Wide Open Spaces," "Without You," and "Travelin' Soldier."
