Sidney was strongly associated with New York, where most of his films were made.
And he was close to the city's mayor, Michael Bloomberg, who also expressed sadness at his passing, adding: "He touched countless lives through his work."
Musician Quincy Jones, who scored music for some of Sidney's movies and claimed that the film-maker had even launched his career in movies with The Pawnbroker, said he was devastated to learn of his death.
Meanwhile, actor Phillip Seymour Hoffman, who starred in Sidney's last ever film, 2007's Before the Devil Knows You're Dead, called him a "true master".
Sidney passed away at his Manhattan home of lymphoma, his step-daughter confirmed on Saturday.
Tributes for Sidney Lumet
- Woody Allen - "Sidney was definitely the quintessential New York film-maker. I'm constantly amazed at how many films of his prodigious output were wonderful and how many actors and actresses had their best work under his direction. Knowing Sidney, he will have more energy dead than most live people."
- Martin Scorsese - "The death of Sidney Lumet really marks the end of an era. He had a unique gift with actors, an unusually dynamic feeling for drama, and a powerful sense of place, of the world of the picture. It's hard to imagine that there won't be any more new pictures by Sidney Lumet. All the more reasont o take good care of the ones he left behind."
- Al Pacino - "Sidney Lumet will be remembered for his films. He leaves a great legacy, but more than that, to the people close to him, he will remain the most civilized of humans and the kindest man I have ever known. This is a great loss."
- Quincy Jones - "Sidney was a visionary film-maker whose movies made an indelible mark on our popular culture with their stirring commentary on our society. Future generations of films-makes will look to Sidney's work for guidance and inspiration but there will never be another who comes close to him."
- Michael Bloomberg - "Today, we lost one of the great chroniclers of our city, a prolific filmmaker who embraced New York as his home. He touched countless lives through his work."
- Phillip Seymour Hoffman - "He was a true master who loved directing and working with actors like no other."