The writer was responsible for plays including Equus – revived in 2007 with Daniel Radcliffe starring alongside Richard Griffiths in the West End – Amadeus (soon to be revived at the National Theatre), Five Finger Exercise and Black Comedy.
Over the course of his extensive career, Shaffer wrote more than 18 plays, and won many awards including a Tony for Equus and a Golden Globe for his adapted screen play of Amadeus, for which he also won the best adapted screenplay Oscar.
The National Theatre released a statement: "It is with great sadness that we learn of the death of Sir Peter Shaffer, CBE. He was an extraordinary writer, closely associated with the National Theatre."
Rufus Norris, Director of the National Theatre, said: "Peter Shaffer was one of the great writers of his generation and the National Theatre was enormously lucky to have had such a fruitful and creative relationship with him. The plays he leaves behind are an enduring legacy."
Shaffer's agents, Macnaughton Lord Representation, also released a statement: "It is with great sorrow that we must announce the death of our friend and client, Sir Peter Shaffer CBE whilst on a visit to Ireland with friends and family. He was 90.
"Peter was one of the true Greats of British Theatre as well as a wonderful friend, wickedly funny man and sparkling raconteur whose lifelong passion for his own art was matched by his love for music, painting and architecture."
They wrote that the writer passed away surrounded by his family and his friend and American agent Dennis Aspland.
Peter is survived by his brother, Brian, nephews Milo and Mark and nieces Cressida and Claudia, whose father and Peter’s twin, the playwright and screenwriter, Anthony Shaffer, died in 2001.
We're hugely saddened to hear of the loss of a true great. Sir Peter Shaffer CBE, 1926-2016. https://t.co/aZ8GJujrsX pic.twitter.com/GCHeJWdePF
— National Theatre (@NationalTheatre) June 6, 2016