The tragic incident took place on a New Mexico film set during filming for the 19th Century western Rust.
Police in the US state said Mr Baldwin discharged the weapon which killed the woman who was the director of photography and seriously injured the male film director.
Sheriff’s deputies were dispatched to Bonanza Creek Ranch on Thursday at around 13:50 local time (19:50 GMT) after receiving an emergency call about a shooting on set.
The director of photography was taken to hospital however, died from her injuries. The film director is understood to have received emergency care.
The woman has been named as Halyna Hutchins, 42, who was working as director of photography. The man being treated is Joel Souza, 48, the film’s director.
Ms Hutchins was from Ukraine and grew up on a Soviet military base in the Arctic Circle. She studied journalism in Kyiv, and film in Los Angeles. She was named a “rising star” by the American Cinematographer magazine in 2019.
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A spokesperson for Mr Baldwin told AP news agency the incident involved the misfiring of a prop gun with blanks.
Police are still investigating the incident at Bonanza Creek Ranch, a popular filming location, and no charges have been filed.
A Santa Fe sheriff spokesman said Mr Baldwin had spoken with detectives, according to a statement to AFP news agency.
Mr Mortimer who was the director of the 2020 action film Archenemy, which Ms Hutchins was director of photography of, tweeted: “I’m so sad about losing Halyna. And so infuriated that this could happen on a set.
“I was lucky to have known her and to have worked with her.”
In a statement, the International Cinematographer’s Guild said Ms Hutchins’ death was “devastating news” and “a terrible loss”.
In a joint statement, Guild president John Lindley and executive director Rebecca Rhine said: “The details are unclear at this moment, but we are working to learn more, and we support a full investigation into this tragic event.”
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