Last month, German tabloid BZ published images of Alexandra, 30, kissing estate agent Sammy Brauner, 41, the son of a German movie producer, reported imdb.com.
Kingsley was quoted as saying: "It came at a very, very vulnerable time for me and I was deeply, deeply shocked because until then I had no idea.
"It's very difficult for a man to learn on the Internet that his wife has a new boyfriend.
"Tragically I had to file for divorce. I love her and I don't know what the future holds. What can I say? I'm very hurt. I'm feeling terrible disappointment and grief."
Kingsley met his third wife in 2002 when he was attending the Berlin film festival. They wed in September 2003.