Judd's spokeswoman confirmed a report that the 44-year-old actress and her 39-year-old husband were ending their marriage.
The star of such films as Double Jeopardy and Kiss The Girls said in a statement that the pair would "always be family" and continue to cherish their relationship based on love, integrity and respect.
Last year Judd starred in the ABC TV series Missing and attended the Democratic National Convention as a Tennessee delegate.
The couple wed in a private ceremony in Scotland in 2001.
From Bathgate, Franchitti is a Celtic fan. He and Judd were were seen together in the stands at Celtic Park in December when Celtic beat Barcelona in the Champions League qualifiers.
Franchitti has won the Indianapolis 500 race three times. He is a cousin of Scottish Force India F1 driver Paul di Resta.
The couple's statement 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."
Shortly after the news broke in the US, Judd tweeted: "Family forever. @dariofranchitti."
Franchitti later responded with a tweet of his own: "@ashleyjudd family forever."