Besides Tharanga, the rest of the team was fined 10 percent for the same offence in Tuesday's match.
Match referee Andy Pycroft imposed the fine after Tharanga's side was ruled to be one over short of its target when time allowances were taken into consideration, according to an International Cricket Council (ICC) statement.
"In accordance with Article 2.5.1 of the ICC Code of Conduct for Players and Player Support Personnel, which relates to minor over-rate offences, players are fined 10 percent of their match fees for every over their side fails to bowl in the allotted time, with the captain fined double that amount," the statement read.
"As such, Tharanga has been fined 20 percent of his match fee, while his players have received 10 percent fine. Tharanga pleaded guilty to the offence and accepted the proposed sanction, so there was no need for a formal hearing," it added.
The charge was laid by on-field umpires Ranmore Martinesz and Raveendra Wimalasiri, third umpire Ruchira Palliyaguruge and fourth official Deepal Gunawardene.