On Thursday, the Santa Fe Sheriff's Department announced in a press release that Souza, 48, was injured on set after Baldwin, 63, discharged a prop firearm. Officials previously said Souza was undergoing treatment for his injuries at Christus St. Vincent's hospital Thursday night.
In response to Patricia Arquette's social media condolences following the accident, Fisher responded, "Director Joel Souza told me he's out of hospital."
Director Joel Souza told me he’s out of hospital.
— Frances Fisher (@Frances_Fisher) October 22, 2021
The actress later asserted again that Souza was no longer in the hospital and was released "hours ago."
Representatives for Joel Souza did not immediately respond to PEOPLE's request for comment.
Ron Adar/SOPA Images/Shutterstock; Mark Sagliocco/Getty Images
Along with the Rust director's injury, Thursday's tragic accident killed cinematographer Halyna Hutchins, 42, who was airlifted to the University of New Mexico Hospital and later died from her injuries, according to the sheriff's department.
Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories.
Following Hutchins' death, directors, actors and those in the film industry paid tribute to the late cinematographer.
"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," wrote actor Joe Manganiello on Instagram, "and she was a fantastic person."
So far, no charges have been filed. The investigation into the incident remains ongoing.
Mark Sagliocco/Getty Images; Mat Hayward/Getty Images; Ron Adar/SOPA Images/Shutterstock Alec Baldwin; Halyna Hutchins; Joel Souza
The film set has now been shut down, with production indefinitely paused, according to the film's production company, Rust Movie Productions LLC.
"The entire cast and crew has been absolutely devastated by today's tragedy, and we send our deepest condolences to Halyna's family and loved ones," Rust Movie Productions LLC said in a statement. "We have halted production on the film for an undetermined period of time and are fully cooperating with the Santa Fe Police Department's investigation. We will be providing counseling services to everyone connected to the film as we work to process this awful event."
The film, written and directed by Souza, is reportedly set in 1880s Kansas. Baldwin stars as an infamous outlaw who goes on the run with his 13-year-old grandson after the teenager is convicted for the accidental murder of a local rancher and sentenced to hang, according to Deadline.