Ziemba succeeds Kathy Najimy, who departed the production to begin filming a TV project.
The cast also stars Annette O’Toole, Ariel Woodiwiss, Reg E. Cathey, Steve Mellor, Tommy Crawford and Danny Rivera.
Previews began Sept. 29 with opening night on Oct. 11.
"Set in the near future, Mary (played by Annette O'Toole) and Joseph (Stephen Mellor) have come to Homeland Security because their protesting son, Chris, has been taken into custody during the latest crackdown," according to press notes. "They put their case before Pontius Pilate (Reg E. Cathy)."
The design team includes Kate Sinclair Foster (sets), Brian Aldous (lights), and Claudia Brown (costumes).
The Flea is located at 41 White Street between Broadway and Church, three blocks south of Canal. Tickets are available by calling (212) 352-3101 or online at www.theflea.org.