Herath will be replaced by off-spinner Tharindu Kaushal, organisers said in a statement.
Sri Lanka chief selector Sanatah Jayasuriya had said two days ago that he expected the 36-year-old Herath to be fit enough to play their quarter-final.
"Herath needed stitches into the index finger of his bowling hand in the match against England and because he has not trained properly for 16 days, and is still unfit, he has been ruled out of further participation in the tournament," the statement said.
Sri Lanka play South Africa later on Wednesday in Sydney, with the winner of that match to head to Auckland for the semi-final against the winner of the fourth quarter-final between New Zealand and West Indies.
(Reporting by Greg Stutchbury in Wellington; Editing by Ian Ransom)
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