Muralitharan, 38, who is also the team's vice captain, was injured during Friday's opening match against New Zealand in Guyana, which Sri Lanka lost by two wickets.
"Clinical tests revealed a grade one strain of his right adductor muscle," team physiotherapist Tommy Simsek said in a statement released by Sri Lanka Cricket in Colombo.
"Murali has been advised to rest for two to three weeks." Muralitharan, who is the most successful bowler in history with a record 792 Test and 512 one-day wickets, took two wickets for 25 runs against New Zealand.
His replacement will be announced soon by the selectors in Colombo, a Sri Lanka Cricket spokesman said. Sri Lanka take on Zimbabwe in their last group B match in Guyana later on Monday, a game the 2009 World T20 runners-up must win to stay in the 12-nation tournament.
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