The Oscar winner was known for her roles in films including the 1987 comedy Moonstruck and 1989 drama Steel Magnolias.
Cher who starred alongside Dukakis in Moonstruck, labelled her an “amazing” actress in a tribute shared on social media.
The singer and actress added: “Olympia Played My Mom In Moonstruck,& Even Though Her Part was That Of a Suffering Wife, We [laughed] ALL The Time.
“She Would Tell Me How MUCH She Loved Louis, Her “Handsome Talented, Husband”.
“I Talked To Her 3Wks Ago. Rip Dear One.”
Actress and producer Viola Davis labelled Dukakis a “consummate actor”.
In a tweet, she added: “You made all around you step up their game.
“A joy to work with. Rest well. ‘May flights of angels sing thee to thy rest’.”
British actor Tony Maudsley said he was “so incredibly sad” to hear of Dukakis’ death as he reflected on his experiences of working with the actress.
“A genius Oscar winning actress from whom I learned so much in my early career,” he said.
“Such happy memories of working alongside her in A Life For A Life: The True Story of Stefan Kiszko, The Intended and My Beautiful Son.
“I did my very first TV interview with her at my side, squeezing my hand because I was so scared.”
Star Trek star George Takei also paid tribute to Dukakis in a tweet.
He wrote: “Olympia Dukakis has departed our company.
“We were Moonstruck by her, as she told us great Tales of the City.
“A true Steel Magnolia within a more common forest.
“Ah, what a life force, her later years her best. Rest now among the heavens, Olympia.”
Better Call Saul star Michael McKean said Dukakis was “a great actress who loved the work and loved the theatre”.
He added: “She was the acting teacher who spoke to me (and many, many others) with clarity and humor and NO censor.
“She would tell us: don’t forget that the reason you wanted to do this was that it looked like fun.
“And it is. Amid the sweat and the angst, don’t forget the fun. Rest in peace, Olympia.”