The left-handed batsman achieved both feats on day three of the ongoing second Test against England at the Galle International Stadium on Sunday.
Sri Lanka has picked four specialist spinners to play Australia in the upcoming ODI tri-series as well as Twenty20 Internationals.
Sri Lanka's Tillakaratne Dilshan was among the leading players who went unsold at the IPL auction last week and now the most dangerous batsman is doubtful for the Asia Cup.
Angelo Mathews was replaced Lasith Malinga as captain of the Sri Lankan cricket team for the International Cricket Council World Twenty20.
Sri Lanka defeated Afghanistan by 34 runs in the ICC Men's Cricket World Cup match at Sophia Gardens in Cardiff on Tuesday.
This is Tharanga's second ban in recent times after he suffered a similar two-match ban for slow over-rate in the Champions Trophy when he had led the side against South Africa in the absence of then-skipper Angelo Mathews.
It remains to be seen if reserve opener Ajinkya Rahane, the only player not to get a game in this series, would be included in place of Rohit Sharma or Shikhar Dhawan.
The visitors have a 2-0 lead in the series and can wrap up the contest with another win here before leaving for the last leg of the tour in Colombo.
Considered one of the greatest finishers in 50-overs cricket, Dhoni will join India's elite 'Club 300', which has Sachin Tendulkar (463), Rahul Dravid (344), Mohammed Azharuddin (334), Sourav Ganguly (311) and Yuvraj Singh (304).
IPL Action VIII: These players went unsold