The couple stunned fans by announcing plans to end the relationship on Tuesday.
A joint statement given to People.com read: "We have mutually decided to end our marriage. We'll always be family and continue to cherish our relationship based on the special love, integrity, and respect we have always enjoyed."
There were no signs of trouble when the Double Jeopardy star spent her anniversary with the racecar driver on 12 December as she tweeted: "Experiencing a profoundly poignant, unique, beautiful 11th Wedding Anniversary with my Love, Dario Franchitti. Family is irreplaceable."
Judd married Franchitti in a private ceremony in his native Scotland in 2001 after a two-year engagement.
Her half-sister, country singer Wynonna, was maid of honour, while the groom's brother Mario was the best man.