The move came Friday, two days after Tra was dismissed from the Party for "serious wrongdoing" amid investigations into stock market manipulations that began in March.
Dao joined HoSE at its inception in 2000 and was appointed deputy director for auction and listing management in 2013.
After the change the HoSE management board has four members, Dao himself and three deputy directors, Ngo Viet Hoang Giao, Nguyen Vu Quang Trung and Tram Tuan Vu.
On Friday, State Securities Commission chairman Tran Van Dung was dismissed and temporarily replaced with Deputy Finance Minister Nguyen Duc Chi.