Jason Miller, a pipe rigger and lamp operator on the film's wrap team, is trying to "save his arm from amputation" after he was bitten by a brown recluse spider, according to a GoFundMe page launched on Miller's behalf.
"In a matter of days he experienced severe symptoms including necrosis of his arm and sepsis. He has been hospitalized and endured multiple surgeries each day as doctors do their best to stop the infection and try to save his arm from amputation," Miller's family wrote in the campaign.
A rep for the Rust production team was not able to provide a comment for PEOPLE at this time.
"It will be a very long road to recovery for Jason if the medical team at Abq Lovelace is able to save his arm," they added. "If under worse circumstances he loses his arm, this is a life-changing and devastating event for Jason and his family. For any who are able to support and offer contributions to help Jason get through this painful and challenging time, it would be incredibly helpful and greatly appreciated."
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Since it was launched on Friday, the campaign has raised more than $8,400, surpassing the fundraiser's initial $5,000 goal.
After PEOPLE confirmed that one crew member died and another was critically injured last month on the New Mexico set of Rust, the Santa Fe Sheriff's Department said in a statement that cinematographer Halyna Hutchins and writer/director Joel Souza were "shot when a prop firearm was discharged by Alec Baldwin, 63, producer and actor."
Authorities responded to a 911 call from the set at Bonanza Creek Ranch at around 1:50 p.m. local time on Oct. 21. Hutchins, 42, was airlifted to the University of New Mexico Hospital where she died of her injuries. Souza, 48, was released the following day from Christus St. Vincent Regional Medical Center where he underwent treatment for his injuries.
"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," Baldwin said the day after the shooting in a statement on Twitter.
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"I'm fully cooperating 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," he continued. "My heart is broken for her husband, their son, and all who knew and loved Halyna."
Sources from the production, which has since been halted amid an investigation, told PEOPLE they "didn't feel safe" on the Santa Fe set. The crew even organized a walkout over unsafe working condition, the morning of the shooting incident.
A spokesperson for the movie's production company, Rust Movie Productions, LLC, told PEOPLE previously: "The safety of our cast and crew is the top priority of Rust Productions and everyone associated with the company. Though we were not made aware of any official complaints concerning weapon or prop safety on set, we will be conducting an internal review of our procedures while production is shut down. We will continue to cooperate with the Santa Fe authorities in their investigation and offer mental health services to the cast and crew during this tragic time."