Velappan was the longest-serving general secretary in the confederation's 64-year history, heading up the administrative arm from 1978 until his retirement in 2007. He was 83.
"On behalf of the entire Asian football family, I send my condolences and heartfelt sympathy to the family of one of the most important architects of growing the game in Asia," said Sheikh Salman.
"Peter served Asian football with passion and professionalism and the news of his passing will shock and sadden all those who are involved in our great game on this continent.
"He deserves immense credit for everything that he achieved with the AFC and beyond."
Velappan served under three presidents at the AFC after joining the confederation from the Football Association of Malaysia.
He was also coordination director for the organising committee for Asia's first World Cup, held in South Korea and Japan in 2002.
(Reporting by Michael Church, Editing by Sudipto Ganguly)
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