The show is a parody of the Oscar-winning thriller, "The Silence of the Lambs."
Producers said after they announced the musical's closing, "ticket sales have unexpectedly soared, shattering all previous box office records for the show so far."
An open-ended extension has been announced to accommodate the demand.
Originally announced as a strictly limited engagement through Aug. 13, 2011, "Silence! was extended numerous times and transferred theaters twice, ultimately landing at the new Elektra Theatre in the heart of Times Square.
The current cast of the show includes David Ayers, Pamela Bob, Harry Bouvy, Ashlee Dupre, Natalie Joy Johnson, Howard Kaye, James Moye, Topher Nuccio, Ronica V. Reddick, Sam Rogers, Kimberly Stern, and Doug Trapp.