She spent almost eight hours in jail before being released on $1,000 bail.
According to the arrest affidavit, Metro Nashville Police Department officers responded to the couple's home just after 2 a.m. for a report of a possible domestic disturbance.
Branch, 39, told police she and her husband "are having marital problems" and said she slapped Carney in the face once or twice during an argument, according to the affidavit.
Carney had no visible injuries, an officer wrote in the report.
In a separate interview with officers, Carney told police his wife slapped him.
Branch was booked into jail at 4:30 a.m. on a misdemeanor domestic assault charge, online records show, and was released just before noon.
Representatives for Branch did not immediately respond to USA TODAY for comment regarding her arrest.
Police arrested Branch on the same day the singer confirmed to USA TODAY she split from Carney. The “Everywhere” singer-songwriter married the rock drummer in April 2019. They share two children, one who is an infant.
"To say that I am totally devastated doesn't even come close to describing how I feel for myself and for my family. The rug has been completely pulled from underneath me and now I must figure out how to move forward," Branch wrote in a statement released to USA TODAY Thursday night. "With such small children, I ask for privacy and kindness."
Court documents show Branch is slated to appear in court Nov. 7 for a settlement.
Contributing: Matthew Leimkuehler, The Tennessean
Natalie Neysa Alund covers trending news for USA TODAY. Reach her at email@example.com and follow her on Twitter @nataliealund. Reach Tennessean reporter Molly Davis at firstname.lastname@example.org or on Twitter @mollym_davis.
This article originally appeared on USA TODAY: Michelle Branch arrested for assault amid husband Patrick Carney split