"This is an unimaginable tragedy," Plaza shared with Entertainment Weekly. "We are deeply grateful to everyone who has offered support. Please respect our privacy during this time."
Official sources confirmed Baena's passing to EW on Saturday, attributing the cause to suicide by hanging.
Plaza, who was scheduled to present at the Golden Globes, did not appear at the event.
During the ceremony, director Brady Corbet offered condolences, stating, "My heart is with Aubrey Plaza and the family of Jeff Baena."
An outpouring of grief has emerged from those who knew and worked with Baena.
Actress Alison Brie, a frequent collaborator, shared photos with Baena on Instagram, writing "Rest in peace my friend" over images from their projects together.
Actress Molly Shannon, who starred in Baena's film "Spin Me Round," posted a photo with the director alongside a broken heart emoji.
Actor Adam Pally, who led Baena's 2016 film "Joshy," shared a heartfelt tribute on Instagram, describing Baena as "a talented director with impeccable taste and vision... a connector of people... and most important to me a friend."
Plaza and Baena began their relationship in 2011, marrying a decade later in 2021. Plaza appeared in several of Baena's films, including "Life After Beth," "The Little Hours," and "Spin Me Round." The pair also collaborated on the anthology series "Cinema Toast," with Plaza making her directorial debut.
Reflecting on their work together in 2021, Plaza told PEOPLE, "It was great... very hectic while we were making the show because we were quarantined... our house became this strange post-production facility and he's downstairs on his Zooms or on his sessions and I'm upstairs editing, we're just going back and forth."
Plaza described the experience as "very us. We were not baking sourdough bread, but we were sifting through hours of old movies and footage and re-cutting them together and just letting our minds go on a trip. So it was great."