She died in Sant Pau hospital in Barcelona.
The "Gran Teatre del Liceu" opera house in Barcelona, where Caballe performed more than 200 times, described her as "one of the most important sopranos in history". She was particularly admired for her purity of voice, vocal shadings and exquisite pianissimos.
Tenor Jose Carreras told Catalunya Radio that the world of opera had lost its "best soprano", saying: "Of all the sopranos that I have heard live, I have never heard anyone like Montserrat".
Madrid's Teatro Real said it would dedicate Saturday's performance of "Faust" to the memory of Caballe, lauding the "singular beauty of her voice" and her prodigious technique.
In a brief excursion into pop music, she dueted with Freddie Mercury on the song "Barcelona", which was a hit in 1987, accompanied by an album of the same name.
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Renowned for her performances of Italian opera, she also worked with the late tenor Luciano Pavarotti.
FILE PHOTO: Spanish opera singer Montserrat Caballe laughs during a concert at Konzerthaus in Vienna, Austria June 22, 2011. "Her voice and her kindness will always remain with us". "We are very sorry for her loss", the royals said in a tweet.
Caballe's worldwide breakthrough came in 1965 when she replaced Marilyn Horne in a semi-staged performance of Donzietti's Lucrezia Borgia at New York's Carnegie Hall, to which she earned a 25-minute standing ovation.
Her performance that night catapulted her the world stardom throughout the opera scene.
Caballe's big break came in 1965 when she stepped in for another singer in the notoriously hard role of Lucrezia Borgia in Donizetti's opera in NY.