HollywoodReporter has the official press release from 20th Century Fox concerning director Darren Aronofsky (Black Swan) leaving the The Wolverine. Darren sited personal reasons as the production would spend close to a year in Japan and away from his son. Even with the disaster over in Japan the studio is still moving forward with the film shooting a majority of it on location there.
It's a testament to the commitment both the studio and Hugh Jackman have to the movie being shoot in Japan. As many studios might be scared off to start new productions there during the recovery effort. It's interesting they haven't named a new director but it would have to be named soon as the production is set for July with a November-December 2012 release date pending. A recent casting call-sheet for the film was released online so they must someone replace Darren.
My choice to take on the film would be Matt Reeves who is best known for Cloverfield and more recently Let Me In. Reeves had been in the running to take the director's chair before Aronofsky was hired. I assume it's very possible as Reeves has yet to announce his next film and seems like he could jump right in if Fox decides to go with him. David Slade who was also a candidate was just selected to direct their Daredevil reboot so he's likely now out of the running. The real wild card would be if Matthew Vaughn is offered the film as Bryan Singer is busy with Jack The Giant Killer. Vaughn has also yet to announce his next film and will be finished with X-Men First Class come July. I'm sure the studio will announce a new director very soon as they must have a backup.