Carter had extended his contract with the production four times. Producers are billing his departure as an extended leave of absence, with the intent that Carter will return to the production following the conclusion of his open-ended tour.
"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 cast also features John Davidson as Bellamy, Addi McDaniel as Luisa, George Dvorsky as El Gallo, Tom Flagg, Michael Nostrand, Daniel Rowan and Dan Sharkey.
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.
The Fantasticks originally opened at the Sullivan Street Playhouse in May 1960 and closed Jan. 13, 2002. The original company included Wedding Singer star Rita Gardner and the late Jerry Orbach.
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.