Gutierrez was in the process of casting the show when he died in his sleep of respiratory failure at the age of 53.
Opening is scheduled for April 29 at the Lucille Lortel Theatre, 121 Christopher Street, after previews from April 20. Engaged will run through May 16 with a possible extension to May 23.
Engaged was penned in 1877 by half of the famous Gilbert and Sullivan team. The play will end the TFANA 25th season.
According to TFANA, Gutierrez had cast Danielle Ferland, Maggie Lacey, John Horton, David Don Miller and Sloane Shelton at the time of his death, and had assembled a production team of John Lee Beatty, sets; Catherine Zuber, costumes; Rui Rita, lighting; and Guy Sherman, sound. Further casting is yet to come.
Hughes scored an Off-Broadway hit last fall with The Beard of Avon at New York Theatre Workshop. His next assignment is Frozen at MCC, with Swoosie Kurtz, Brian F. O’Byrne and Laila Robins in the cast. Hughes was artistic director of the Long Wharf Theatre from 1997 to 2001. For more information, visit www.tfana.org.