Speaking at the launch of the network's 50th anniversary season, he said the retrospective would enable listeners to come to terms with "the best of 20th century culture" - which, musically at least, is notoriously among the most difficult.
Details are yet to be worked out, but Mr Kenyon said the two-and-a-half year project - which would take up a number of hours of the station's weekly output - would be "music-based" and involve a variety of different orchestras, not just the five funded by the BBC.
He revealed the initiative after launching Radio 3's plans to celebrate its 50th anniversary on 29 September with a series of live broadcasts from BBC orchestras, a new production of Bernard Shaw's Man and Superman directed by Sir Peter Hall, and five new radio poems by leading poets.
The date will also be marked by a specially commissioned history of the network - which began life as The Third Programme, broadcasting only in the evenings - by Humphrey Carpenter. Mr Carpenter has been in the limelight recently over his biography of Lord Runcie, the former Archbishop of Canterbury.
Mr Kenyon made a joking reference to the fact that Lord Runcie, who has distanced himself from some of his comments in the book, expected the biography to be published after his death.
"Humphrey came in with the history of Radio 3 and put it on my desk for me to sign. I read what it said: 'I have done my best to die before this book is published.' I thought: 'This is a bit steep, I wasn't born when The Third Programme was launched'," he said, to laughter.
"All of us only hold this remarkable enterprise in trust for the audience and the audience know jolly well they run us and not the other way round. It's always been the case," he continued more solemnly.
"The Third Programme was one of the greatest and most enduring creations of the BBC in the post-war period. Its cultural programming had a permanent impact on our national life and influenced generations of listeners. Even though it broadcast only in the evenings, its range and scope were extraordinary."
Among the programmes on the anniversary day of 29 September will be Mr Carpenter in conversation with Mr Kenyon, the BBC National Orchestra of Wales performing Ravel's Daphnis and Chloe live from Cardiff, the BBC Philharmonic in the world premiere of Roberto Gerhard's Soirees de Barcelone, Osmo Vanska conducting the BBC Scottish Symphony Orchestra's performance of Shostakovich's Symphony No 1 live from Glasgow, and a repeat of the 1957 recording of Beckett's first radio play, All That Fall.
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