A spokesperson for Baldwin said there was an accident on the set involving the misfire of a prop gun with blanks.
Production has been halted on the film, which was being directed by Souza with Baldwin producing and starring in it.
Halyna Hutchins, 42, director of photography, and Joel Souza, 48, director, were shot when a prop firearm was discharged by Alec Baldwin, 68, producer and actor,” it said.
Filming for Rust was set to continue into early November, according to a news release from the New Mexico Film Office.