Greece's Culture Minister Lina Mendoni in a statement said Papas was "majestic" and "the personification of Greek beauty on the cinema screen and theatre stage".
Her cause of death was not immediately known, but the actor had Alzheimer's Disease and had been frail for some time.
One of Greece's most renowned actors, Papas appeared in over 60 films in a career spanning nearly six decades.
On screen and stage she starred with A-list partners, including Richard Burton, Kirk Douglas and Jon Voight.
"Ordinary actors have trouble sharing the screen with her," the late film critic Roger Ebert wrote in 1969.
Widely known as Pappas but personally preferring a single 'p' in her surname, the actor was born Irene Lelekou in 1929 in the village of Chiliomodi near Corinth, into a family of schoolteachers.
Gifted with a deep voice, piercing eyes and a chiselled face likened to the Caryatid statues of ancient Greece, Papas began performing at the age of 15 in local cultural events before studying drama in Athens.
She made her cinema debut in the 1948 Greek drama "Fallen Angels", and later broke onto the international scene with "Dead City", the first Greek movie shown at the Cannes Film Festival in 1952.
'Not looking for a career'
"The Guns of Navarone" in 1961, in which she starred alongside Gregory Peck and Anthony Quinn, as a brooding Greek guerrilla fighter, was a landmark role in Papas's career.
She would again partner up with Quinn in 1964's "Zorba the Greek", another timeless classic.
"I left Greece to discover where the best acting was. I wanted to learn. I was not looking for a career," she told state TV ERT in 2002.
"If you do your job well, a career comes on its own."
In 1969, she played the widow of a murdered lawmaker in Costa-Gavras's Oscar-winning drama "Z".
Papas won several awards, including best actress at the 1961 Berlin Film Festival and the 2009 Golden Lion for lifetime achievement award in Venice.
Yet, she described herself as a "coward" who turned to theatre to overcome timidness and struggled to reconcile her fiery on-screen persona with her real self.
'Fame gave me nothing'
"Fame gave me nothing," Papas said in a 2003 interview with Greek daily Eleftherotypia.
"In contrast, it destroyed my private life. Because the person who will approach me, let's say sexually, has already fallen in love with my image."
In 2004, she revealed a secret, long affair with Marlon Brando in the 1950s.
"We had a love story," she told Italy's Corriere della Sera daily.
At the age of 18, Papas married her acting tutor Alkis Papas. They had no children and soon divorced, but she kept her husband's surname.
In her final years, she lived near Athens' Acropolis, cared for by a niece as she battled Alzheimer's.