Santa Fe County Sheriff's officials said Halyna Hutchins, director of photography for the movie "Rust," and director Joel Souza were shot.
Hutchins, 42, was airlifted to hospital, where she was pronounced dead by medical personnel, authorities said.
Souza, 48, was taken by ambulance to a medical centre where he is undergoing treatment for his injuries.
Production has been halted on the film.
A spokesperson for Baldwin said there was an accident on the set involving the misfire of a prop gun with blanks.
Deputies responded about 2 pm to the movie set at the Bonanza Creek Ranch after 911 calls came in of a person being shot on set, sheriff’s spokesman Juan Rios said.
The ranch has been used in dozens of films, including the recent Tom Hanks Western “News of the World.”
He said detectives were investigating how and what type of projectile was discharged.
No charges have been filed. Police said witnesses continue to be interviewed by detectives.
The Santa Fe New Mexican reported the 63-year-old Baldwin was seen Thursday outside the sheriff's office in tears.
The International Cinematographers Guild confirmed that the woman fatally shot was Hutchins, a cinematographer.
"The details are unclear at this moment, but we are working to learn more, and we support a full investigation into this tragic event," guild president John Lindley and executive director Rebecca Rhine said in a statement.
Hutchins, 42, was director of photography on the 2020 action film "Archenemy," starring Joe Manganiello. A 2015 graduate of the American Film Institute, she was named a "rising star" by American Cinematographer in 2019.
"I'm so sad about losing Halyna. And so infuriated that this could happen on a set," said "Archenemy" director Adam Egypt Mortimer on Twitter. "She was a brilliant talent who was absolutely committed to art and to film."