Police in the US state said Mr Baldwin discharged the weapon during filming for the 19th Century western Rust.
The woman was taken to hospital but died of her injuries. The man, the film's director, was receiving emergency care.
Detectives are investigating the incident at Bonanza Creek Ranch, a popular filming location.
The woman was identified as 42-year-old Halyna Hutchins, who was working as director of photography. The man being treated is Joel Souza, 48, the film's director.
Police said their investigation remains open and active, and no charges have yet been filed in relation to the incident.
Ms Hutchins was a graduate of the American Film Institute and had been named a "rising star" by American Cinematographer magazine in 2019.
In a statement to Variety magazine, the International Cinematographer's Guild said Ms Hutchins' death was "devastating news" and "a terrible loss".
Police said sheriff's deputies were dispatched to Bonanza Creek Ranch at around 13:50 pm MST (19:50 GMT) after receiving an emergency call about a shooting on set.
Mr Baldwin, 68, is a co-producer of the film and plays its namesake, an outlaw named Rust, whose 13-year-old grandson is convicted of accidental murder.
