The incident happened on the set of “Rust” in the southwestern US state, where Baldwin is playing the lead in a 19th century western.
Halyna Hutchins and Joel Souza “were shot when a prop firearm was discharged by Alec Baldwin,” the sheriff in Santa Fe said in a statement.
Hutchins, 42, was transported to hospital by helicopter but died of her wounds, while Souza, 48, was taken by ambulance and is receiving treatment.
“Mr. Baldwin was interviewed by detectives,” Santa Fe sheriff spokesman Juan Rios told AFP.
“He provided statements and answered their questions. He came in voluntarily and he left the building after he finished his interviews. No charges have been filed and no arrests have been made.”
The Santa Fe New Mexican published pictures of a distraught-looking Baldwin which it said were taken in the parking lot of the set after the tragedy.
The paper said its reporter had seen the actor in tears after he had been quizzed by investigators.
One photograph shows a man, presumed to be Baldwin, doubled over.
A spokesperson from the production told The Hollywood Reporter the “accident” involved the misfire of a prop gun with blanks.
The incident took place at the Bonanza Creek Ranch, a production location near Santa Fe which is popular with Hollywood filmmakers.
Movie sets usually have stringent rules over the use of prop weapons, but accidents have happened.
Most famously, Brandon Lee, the son of martial arts legend Bruce Lee, died during filming of “The Crow” after being shot by a gun that was supposed to fire blanks.
Baldwin co-produces the film and stars as Harland Rust, an outlaw whose grandson is convicted of murder, and who goes on the run with him when the boy is sentenced to hang for the crime.
The 63-year-old posted a photograph earlier yesterday on Instagram showing him apparently on set, dressed in a period costume and with fake blood on his shirt.
“Back to in-person at the office. Blimey... it’s exhausting,” he captioned the picture, which went online several hours before the incident.
A joint statement by John Lindley and Rebecca Rhine of the International Cinematographers Guild said news of Hutchins’ death was “devastating”.
“The details are unclear at this moment, but we are working to learn more, and we support a full investigation into this tragic event. This is a terrible loss, and we mourn the passing of a member of our Guild’s family,” the statement, reported by Variety, said.
Baldwin has been on television and in films since the 1980s.
He starred in a number of high profile movies, including in “The Hunt for Red October” and two iterations of the “Mission: Impossible” franchise, and has also voiced animated characters in hits like “The Boss Baby”.
He garnered new fans with his long-running portrayal of Donald Trump on “Saturday Night Live”, a character that irritated the former president, but won Baldwin a Primetime Emmy.
“Rust” also stars Jensen Ackles (“Supernaturals”) and Travis Fimmel, best known for playing Ragnar Lothbrok in “Vikings”.
The Bonanza Creek Ranch where yesterday’s incident took place has hosted productions including “Hostiles,” “Cowboys & Aliens,” “3:10 to Yuma,” “Appaloosa” and “Longmire.”