10:05 AM PT -- Busch just released a statement on the matter ... saying, "I am heartbroken to confirm that my wife Ashley and I are working to dissolve our marriage. Divorce is a personal and private matter and I hope our privacy will be respected."
Kurt Busch's wife has filed for divorce from the NASCAR star ... saying in court documents, obtained by TMZ Sports, their marriage is "irretrievably broken."
Ashley Busch filed the docs in Florida on May 9 .