Hess, who made her Broadway debut in the 1981 revival of Can-Can, is temporarily stepping into the role while Rebecca Judd takes a leave of absence from The Great White Way's longest-running musical.
Hess previously played the role of the mysterious ballet mistress in the show's national tour in 2008.
Judd will rejoin the New York company March 2; Hess will rejoin the show's national tour April 14.
Phantom, which won seven 1988 Tony Awards including Best Musical, "tells the story of a masked figure who lurks beneath the catacombs of the Paris Opera House, exercising a reign of terror over all who inhabit it. He falls madly in love with an innocent young soprano, Christine, and devotes himself to creating a new star by nurturing her extraordinary talents and by employing all of the devious methods at his command."
The musical has music by Andrew Lloyd Webber, lyrics by Charles Hart (with additional lyrics by Richard Stilgoe) and book by Richard Stilgoe and Lloyd Webber.
For tickets, $26.25-$121.50, call Tele-charge at (212) 239-6200, visit www.telecharge.com or visit The Majestic Theatre box office (247 West 44th Street).
For more information visit www.thephantomoftheopera.com.