Around 10:30 a.m., Baena's assistant contacted the Los Angeles Police and Fire Department.
Upon arrival, authorities confirmed the filmmaker's death.
Sources within law enforcement informed TMZ that suicide is suspected.
However, an official cause of death has not yet been released by the police.
Baena's family is reportedly "devastated" and has requested privacy, according to Deadline.
Married to actress Aubrey Plaza in 2021, the couple had been together for a decade and kept both their engagement and wedding private. Plaza later revealed the marriage in an Instagram post.
Originally from Miami, Baena pursued his filmmaking aspirations in New York and later Los Angeles.
His early career included co-writing the 2004 film "I Heart Huckabees," collaborating with notable actors like Jason Schwartzman and Jude Law.
Baena's breakthrough came with the 2014 zombie comedy "Life After Beth," starring Plaza and John C. Reilly.
The film premiered at Sundance and was nominated for the Grand Jury Prize.
Plaza has spoken about the benefits of having a partner in the same industry, highlighting the mutual understanding and support.
Throughout his career, Baena received multiple award nominations for his writing and directing.
His film "Joshy" earned him another Grand Jury Prize nomination in 2016.
"The Little Hours" was nominated for the Audience Award at the 2017 Edinburgh International Film Festival.
Baena also ventured into television, creating, writing, directing, and executive producing the Showtime series "Cinema Toast."