The show, which was written by and stars Sharon Horgan and Holly Walsh, focuses on a woman called Helen who is falsely imprisoned for the murder of her boss.
Saunders has now joined the cast and will play the prison governor, Chortle reports.
Her character is described as "a sexual Margaret Thatcher" who is "probably even more psychotic than any inmate in [the prison] Broadmarsh".
Call The Midwife star Bryony Hannah will play Helen's arsonist cellmate, while Spy's Tom Goodman-Hill will star as one of the prison guards.
Geoffrey McGivern, who was recently seen in This Is Jinsy, has joined the cast as a lawyer, and Lizzie Roper and Susan Calman will play members of a gang. Caroline Quentin will reportedly also have a guest role in the comedy.
Horgan is also currently working on Channel 4 pilot Bad Sugar, which has been penned by Peep Show writers Sam Bain and Jesse Armstrong and also stars Olivia Colman and Julia Davis.
Dead Boss is expected to air on BBC Three in April.