He was India captain Rohit Sharma's opening partner in the home T20 series against Afghanistan earlier this year but his place looked under threat as he struggled for runs in the IPL
Sri Lanka completed their 50 overs more than half an hour behind schedule during the 96-run defeat by the South Africans at The Oval.
"Tharanga pleaded guilty to the offence and accepted the proposed sanction, so there was no need for a formal hearing," the ICC said in a statement.
Tharanga, deputising as captain for the injured Angelo Mathews, will miss Sri Lanka's remaining Group B matches against India and Pakistan.