"I'm looking forward to going on tour and working on my music, but The Fantasticks is my home – I will be back," Carter said in a previous statement.
His replacement has not been announced.
The Fantasticks is the world's longest-running musical, having played a record-breaking run of more than 17,000 performances in Greenwich Village. Harvey Schmidt wrote the music, and Tom Jones penned the book and lyrics.
Book writer and lyricist Jones staged the revival of The Fantasticks, which has choreography by Janet Watson.
The Fantasticks resumed performances Off-Broadway at the Snapple Theater Center's Jerry Orbach Theater June 16, 2008. The Fantasticks is produced by Terzetto, LLC/Catherine Russell and by Pat Flicker Addis and Al Parinello.
For tickets phone (212) 921-7862 or visit SnappleTheater.com.