The confirmation was conveyed to Sri Lanka Cricket (SLC) on behalf of the committee.
Mathews suffered a strain to his right thigh muscle during the side's semi-final victory over New Zealand in Colombo.
Randiv has played in 21 ODIs for Sri Lanka, claiming 22 wickets at an average of 33.5.
The 26-year-old off-spinner from Matara has also represented Sri Lanka in three Test matches and six Twenty20 internationals.
As with all players in the tournament, the eligibility of a replacement player is subject to approval by the ICC before that player can be officially added to the squad.
The event technical committee consists of David Richardson (ICC, chairman), prof. Ratnakar Shetty (tournament director), Campbell Jamieson (IDI representative), Anil Kumble (host nominee), David Lloyd (independent nomination) and Sanjay Manjrekar (independent nomination).
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