The split comes just six months after the pair welcomed their second child together.
"To say that I am totally devastated doesn't even come close to describing how I feel for myself and for my family," Branch expressed in a statement published by People on Thursday. "The rug has been completely pulled from underneath me and now I must figure out how to move forward."
Branch, 39, continued, "With such small children, I ask for privacy and kindness."
Branch is the mother of three, including six-month-old daughter Willie and son Rhys -- who turns 4 on Aug. 28 -- as well as her 17-year-old daughter Owen from a previous relationship.
In a quickly deleted tweet Branch shared on Wednesday night, the singer accused the Black Keys musician of cheating on her over the past several months while she stayed home to care for their infant daughter. The tweet was deleted but not before seen by many fans.
Carney has yet to comment publicly on the split.