Mali, president of Cricket South Africa since 2003, will take on the role for about 13 months until the ICC's 2008 annual conference, the world governing body said in a statement.
Mali takes over from compatriot Sonn, who died on May 27 at the age of 57 following a colon operation.
"I take this assignment as an honour and a big challenge," said 70-year-old Mali, who has stepped down as CSA president.
"I feel lucky to be taking over at a time when the game is in such good shape. It is also a privilege to succeed Percy, somebody who was a good friend and a person who worked so hard for the betterment of this great game," he added in a statement.
ICC chief executive Malcolm Speed welcomed Mali's appointment, saying he was a worthy successor to Sonn.
"Ray is an experienced and skilled administrator, a man of calm assurance and someone who combines a deep love of the game with an understanding of how best to secure its well-being."