Born in Philadelphia, Pennsylvania, she is the daughter of Broadway dancer Mary Zahn and violin maker William Moennig. She is also the niece of actress Blythe Danner and cousin of Oscar winner Gwyneth Paltrow.

Although there has been much speculation surrounding Moennig's sexual orientation due to the on-screen lesbian and transgender roles she has taken, in a 2000 interview with Rebecca Traister of the New York Observer, Moennig identified herself as heterosexual. There is some evidence to the contrary. There was a comment by L Word costar Jennifer Beals in an interview with The Advocate, which lumped Moennig with openly gay staff and cast members: when asked "Do people still assume that you have to be a lesbian to play one on TV?", Beals responded with, "Not at all... I heard a rumor that somebody... assumed I was and I am bisexual. Which was a huge compliment to me, because often I will go to Leisha or Kate or Ilene or Rose Troche most often and ask, 'OK, is this the right