Dan R. Roach, 49, was arrested Thursday in Abilene and charged with three counts of aggravated sexual battery against a child younger than 13 in Nashville, police said.
He was expected to be extradited to Nashville, said police spokesman Don Aaron.
"I am obviously devastated," the 42-year-old country singer said in a statement on her Web site. "Our family will pull together, begin the healing process and hopefully - by the Grace of God - become stronger. We will move forward with our faith, family and our friends to find resolution to this difficult situation."
Aaron said an investigation by the department's sex crimes unit started in February.
Judd cited irreconcilable differences as a reason for divorce in the complaint filed in the Nashville suburb of Williamson County. The couple, who were married in November 2003, have been separated since Feb. 18, according to the complaint.
Roach had been receiving treatment for drug and alcohol addiction at a rehabilitation clinic in Buffalo Gap, Texas, Judd said.
The couple have no children. Judd has children from a previous marriage.
Judd has sold nearly 30 million albums as a solo artist. She sang with her mother, Naomi Judd, as the duo The Judds. Her solo hits include "No One Else on Earth" and "I Saw the Light." Her sister is actress Ashley Judd.
LONDON - Snoop Dogg and Sean "Diddy" Combs were forced to scrap a tour of Britain after authorities denied Dogg a visa, according to a statement Tuesday.
The duo, currently on a European tour, had been expected to play five dates in Britain.
"With late notice of Snoop being denied a visa, time has ran out and it is too late to reconfigure the show," the statement read.
Tour organizers had said the concerts would go ahead without Dogg.
British Home Office rules state that foreign citizens can be barred from entering the country if there were concerns about their presence.
In April 2006, Dogg, whose real name is Calvin Broadus, and five other men were arrested on charges of violent disorder and starting a brawl, and spent the night in jail after trouble flared when some in the rapper's party were denied entry to British Airways' first-class lounge at Heathrow Airport.
Seven officers received minor injuries - mainly cuts and bruises - and one suffered a hand fracture.
Dogg, 35, was previously barred from entering Britain in May 2006.