The Moulin Rouge! star will prepare for the feat at New York's Repertorio Espanol later this month (Jan12).
The show features vivid accounts of the star's life from his humble beginnings in Queens, New York, to his movie successes.
He isn't the only comic to have translated an English-language theatre show for a foreign audience - British funnyman Eddie Izzard has famously performed his stand-up routine in both his native tongue and French for fans in France and Canada.
The Ocean's Thirteen star became the first winner of Sunday's (12Jun11) ceremony in New York, claiming victory over Edie Falco (The House of Blue Leaves), Judith Light (Lombardi), Joanna Lumley (La Bete) and Elizabeth Rodriguez (The Motherf**ker with the Hat) for her role as a frustrated doctor in the fight against AIDS in a revival of the Larry Kramer play.
Taking to the stage at The Beacon Theatre, Barkin hailed her win as the "proudest moment in my career" and paid tribute to her theatre colleagues.
She told the crowd, "Thank you for the way you've embraced me and welcomed me into your community. I am so grateful and so humbled to be in your company."
South Park creators Trey Parker and Matt Stone were also early winners at the 65th Annual Tony Awards, which celebrates the best of Broadway, earning the prize for Best Original Score for their work on The Book of Mormon. The musical is nominated for a total of 14 Tonys.
Host Neil Patrick Harris opened the awards show with a comical song and dance routine titled It's Not Just For Gays Anymore, and stepped into the audience to share the microphone with the likes of TV funnyman Stephen Colbert and model/actress Brooke Shields, although the beauty flubbed her lines three times and had to refer to a cue card to remember her lyrics.
Daniel Radcliffe and Tony nominee John Larroquette performed Brotherhood of Man from their musical How to Succeed in Business Without Really Trying, while John Leguizamo also took to the stage to share a sketch from his one-man show Ghetto Klown.
Guests in the star-studded audience included Al Pacino, Whoopi Goldberg, Hugh Jackman, James Earl Jones and Vanessa Redgrave.
New York Mayor Michael Bloomberg introduced Damon at the bash, which celebrates those who have made "significant contributions" to the Big Apple's entertainment industry.
As he accepted his prize, Damon, who grew up in Boston, Massachusetts but now lives in New York, told the crowd how he and his childhood pal Ben Affleck used to travel to the city for auditions when they were younger: "Our dream was... to actually get a movie someday that shot in New York... I'm just so proud to live here."
Damon has shot a handful of films in New York including 1998 movie Rounders and his recent thriller The Adjustment Bureau.
Colombian-born Leguizamo, who moved to New York City when he was four, took a night off from his Broadway show Ghetto Klown to pick up a prize in recognition of his theatre work.
The evening's most emotional moment came as Sidney Lumet's daughter Jenny accepted the late filmmaker's Lifetime Achievement accolade on his behalf.
She said, "I haven't spoken about Dad in public yet. I miss him."
Lumet, who based many of his movies in New York, passed away in the city in April (11), aged 86.
The Broadway show, created by South Park masterminds Trey Parker and Matt Stone, was named the season's best musical and received trophies for best lyrics, music, director and orchestrations. The quirky and profane musical, about two Mormon missionaries who head to Uganda to promote the faith, is nominated in 14 categories at next month's (Jun11) Tony Awards.
The Drama Desk panel, comprised of theatre journalists and critics, also gave five awards to the revival of Cole Porter musical Anything Goes, including best set design, sound design, musical revival and outstanding actress for Sutton Foster.
A number of Hollywood stars were winners at the ceremony - actress Frances McDormand accepted an acting prize for Good People, while Edie Falco was recognised for The House of Blue Leaves. John Larroquette also went home with a musical acting trophy for How to Succeed in Business Without Really Trying, while John Leguizamo received the outstanding solo performance statue for his one-man show Ghetto Klown.
The star worried his wife Justine would object to material he uses in the play about his life story and force him to scrap it, so he was relieved when she gave him the thumbs up.
And Leguizamo admits it was her opinion which concerned him the most, despite also poking fun at top Hollywood stars such as Al Pacino, Steven Seagal and Kurt Russell in the script.
During an appearance on America's Today show on Wednesday (09Mar11), he says, "The person I was most afraid of was my wife, because I wasn't sure how she was gonna react to it and she saw it and she gave me the OK, but I was really worried about that because I was saying personal stuff...
"Everybody fights, but I took a lot of the big fights we had and put them on the stage so sometimes that can be hard."
Ghetto Klown will officially open at the Lyceum Theatre on 22 March (11).
"STEVEN SEAGAL said he was gonna punch me out. I know he runs like a woman but he hits like a dude. But he's not gonna catch me." Actor JOHN LEGUIZAMO has revealed the action man is unimpressed by some of his jokes in his new Broadway comedy show, Ghetto Klown, in which he pokes fun at a host of Hollywood stars, including Seagal, Al Pacino and Kurt Russell.
The actor will begin previews of Ghetto Klown at Manhattan's Lyceum Theater on 21 February (11).
The show chronicles the early days of Leguizamo's acting career.
The 46 year old star last appeared on Broadway in 2008 when he was part of the ensemble cast in a revival of American Buffalo. He also wrote and appeared in stage show Sexaholix from 2001 to 2003 and he won an Emmy for his monologue in 1998 Broadway comedy, Freak.
His latest show, directed by Fisher Stevens, officially opens for a 12-week run on 22 March (11).