According to Billboard, Hudson has been cast as a nun in an orphanage where the main characters spend some time.
The singer and actress joins previously-announced cast members including Glee star Jane Lynch and Curb Your Enthusiasm's Larry David.
It has already been confirmed that Will Sasso, Sean Hayes and Chris Diamontopoulos will portray the film's three lead characters Larry, Curly and Moe.
Hudson, who rose to fame on the 2004 series of American Idol, has several acting credits to her name, including Sex & The City, The Secret Life of Bees and Dreamgirls.
The Three Stooges is currently in production.