It said Tharanga had claimed that he was given a steroid by a faith healer in Colombo who also treated other international players.
There was no comment from Tharanga, who is not part of the Sri Lankan side currently on tour in England.
Sri Lanka Cricket said that Tharanga would not be available for selection pending the conclusion of the ICC hearing.
He failed the test after Sri Lanka beat New Zealand by five wickets in the World Cup semi-final in March, becoming the first Sri Lankan international player to fail a doping test.
He scored 30 runs in the match.
"The ICC has informed Sri Lanka Cricket that Upul Tharanga has been tested positive for the presence of a prohibited substance during a testing of a urine sample... and a disciplinary charge has been initiated," SLC said.
Sri Lanka's sports ministry has already started its own investigation.
Under ICC rules, Tharanga can seek a test of his "B" sample.
The embarrassment over the failure of the dope test comes amid