Rudetsky and Jack Plotnick are the authors of the show, which ran off-Broadway in 2013.
Barbra Streisand, the subject of the solo send-up, plans to attend a performance during the L.A. run.
Additional performers for the benefit concert have been announced.
Catch stars Andy Karl, LaChanze, Justin Guarini, and more as they brave the sun to sing showtunes.
The show is a fill-in-the-blanks whodunit written by Billy Mitchell.
The long-running hit currently stars NCIS: Los Angeles regular Barrett Foa.
The NCIS: Los Angeles star takes on Jonathan Tolins' comedy for the next two months.
The NYC native takes over Jonathan Tolins' Barbra Streisand-themed one-man show from Christopher J. Hanke.
The awards were presented November 3 at an event hosted by Michael McKean.