The program's musical director Paul Shaffer is guest host in David Letterman's absence. Multiple Tony Award-winner Fierstein stepped into Fiddler earlier this month. His official opening night is Jan. 20 at the Minskoff Theatre.
Andrea Martin is wife Golde opposite Fierstein.
"The Late Show" airs at 11:30 PM (ET) on CBS. Check local listings for channel and time in your area.