The Oscar-nominated Black Swan director released a statement saying that he exited the blockbuster because it would have taken him away from his family for an extended period of time.
Fox had planned to film a large portion of the Christopher McQuarrie-scripted Wolverine, which sees the title character become a samurai, in Japan.
Aronofsky said: "As I talked more about the film with my collaborators at Fox, who have been totally supportive throughout my work on the movie, it became clear that the production of The Wolverine would keep me out of the country for almost a year.
"I was not comfortable being away from my family for that length of time. I am sad that I won't be able to see the project through, as it is a terrific script and I was very much looking forward to working with my friend Hugh Jackman again."
Aronofsky and Jackman worked together on the 2006 sci-fi romance The Fountain.
Fox said that they are "aggressively" drawing up a shortlist of potential replacements for the director; however the studio is yet to officially give the Marvel Comics adaptation a greenlight.
"While we are of course disappointed that Darren can't do The Wolverine, we also understand and respect his reasons," said the studio in a statement. "Having done both The Wrestler and Black Swan with Darren, we know he is an extraordinary talent and we look forward to working with him on other projects in the future.
"Hugh Jackman and Fox both remain fully committed to making The Wolverine. We will regroup and move forward aggressively."
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