"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," Rupert Lord said on his agency's website.
Shaffer died at 5:30 am (0430 GMT) at a hospital outside Cork in southern Ireland following a short illness, Lord said.
"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," said Lord.
He also received an Academy Award nomination in 1978 for the screenplay of "Equus", his 1973 stage play about a psychiatrist treating a young man fascinated by horses.
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His other plays include "Lettice and Lovage" and "The Royal Hunt of the Sun".
"He had been struggling with his health for some time but was both determined and delighted to have been able to celebrate his 90th birthday in Ireland last month with close family and friends," said Lord.