Born and raised in Auckland, New Zealand, Henderson was introduced to acting when the local television program Strangers held an open casting call at his school. He was cast in the series at the age of 13, and has been acting professionally ever since. He went on to star in the New Zealand drama series Shortland Street for three years, winning a New Zealand Television and Film Award in the category of Best Male Dramatic Performance in a Television Show in 1993.

In 1995, Henderson moved to Sydney, Australia, where he landed the role of a young athlete training for the Olympics in the series Sweat. He later made his feature film debut opposite Rahda Mitchell in Kick, a film set in the world of the Sydney ballet. Henderson received an Australian Film Institute Award for Best Performance in a Supporting Role for his work in Kick.

Following that film, Henderson decided to pursue his career in the United States. Moving to New York in 1999, he began a two-year training program at the Neighborhood Playhouse. He also appeared in several stage productions, including the off-Broadway play Ophelia Thinks Harder at the Samuel Beckett Theatre.