The actor, 63, confirmed he is “fully co-operating” with the police investigation after he fired a prop gun on the US set of the Western, killing Hutchins and injuring director Joel Souza.
In a statement posted on his arts foundation’s social media account, Baldwin described the event as a “tragedy” and said he is in communication with Hutchins’s husband.
He said: “There are no words to convey my shock and sadness regarding the tragic accident that took the life of Halyna Hutchins, a wife, mother and deeply admired colleague of ours.
“I’m fully co-operating with the police investigation to address how this tragedy occurred and I am in touch with her husband, offering my support to him and his family.
“My heart is broken for her husband, their son, and all who knew and loved Halyna.”
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.
The 42-year-old was airlifted to University of New Mexico Hospital but she was pronounced dead.
The film’s director, Joel Souza, was also injured but has since been discharged from hospital, according to actress Frances Fisher.
The camera crew for television series His Dark Materials have joined in tributes to Ms Hutchins after the tragedy.
A photograph of a His Dark Materials clapperboard bearing the words RIP Halyna Hutchins was posted on the BBC and HBO programme’s official Twitter page in tribute to the director of photography.
“We were devastated to learn of the tragic passing of Halyna Hutchins in the USA,” the post said.
“Our wonderful camera crew created this on set today to pay tribute to ‘one of us’.”
Hollywood star Dwayne Johnson, also known as The Rock, commented on Hutchins’ last Instagram post, a video she shared two days ago of herself horse-riding on set, writing that a “perk” of working on a Western was that “you get to ride horses on your day off”.
Johnson wrote: “I am so so sorry. Rest easy. My love and strength to your family.”
Magic Mike actor Joe Manganiello, who recently worked with Hutchins on the film Archenemy, also paid tribute to her.
He wrote on Instagram: “I woke up to the messages and read the news and I am in shock. I was so lucky to have had @halynahutchins as my DP on Archenemy.
“She was an absolutely incredible talent and a great person. She had such an eye and a visual style, she was the kind of cinematographer that you wanted to see succeed because you wanted to see what she could pull off next."
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.”