Barbour pleaded guilty in 2008 to two counts of endangering the welfare of a child.
As part of a plea deal, he admitted he fondled and engaged in oral sex with a 15-year-old girl who visited him backstage after a performance of "Jane Eyre" on Broadway in 2001.
The Times said Barbour's departure from the Old Globe's production of "Rocky Horror Show" came days after his past was discussed by San Diego media. However, Old Globe Executive Producer Lou Spisto said in a statement Thursday Barbour left "due to issues with his wife's pregnancy."
"As my amazing wife is progressing through the second pregnancy we've encountered some unexpected issues and I felt it vital to be with my family during this time," Barbour wrote on his Facebook page.
Celebrity Families of 2014 [PHOTOS]