The 49-year-old former all-rounder is accused of failing to co-operate with an investigation by the governing body.
Earlier this month, the ICC said the ACU was investigating serious allegations of corruption in Sri Lankan cricket and has provided a detailed briefing to the country's president, prime minister and sports minister.
The news has rocked Sri Lanka, who are now hosting a one-day series against England, the top-ranked team in the world.
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The ICC said the first charge against Jayasuriya included the "failure to provide accurately and completely any information and/or documentation requested" by the anti-corruption unit.
The ACU probe into corruption in Sri Lanka has been ongoing for over a year.
The charges relate to failure or refusal to cooperate with an Anti-Corruption Unit (ACU) investigation and obstructing or delaying an investigation, including concealing, tampering with or destroying any documentation or other information which may be relevant.
Jayasuriya has been given two weeks to respond with the charges, starting from October 15.
He scored 13,430 runs in the game's One Day format - a total bettered only by Sangakkara, India's Sachin Tendulkar and Australia's Ricky Ponting.