The show was to open during the 2013-14 theater season, but has been pushed back to 2015-16, Variety said.
"I have greatly enjoyed the collaborative process on 'Houdini,'" Jackman said in a statement. "Ultimately, though, I wasn't able to commit to the time this role will require. I have tremendous respect and admiration for the creative team and I wish everyone the best. I know they're well on their way to making something extraordinary."