The 26-year-old princess, riding the local horse Htate Kwet at Wunna Theikdi Equestrian Field, collected 53.810 points. The gold medal went to Malaysia's Praveen Nair Mathavan who collected 67.405 points.
"I want to thank my friends for giving me the support and the people in social media who follow me as well as media members and the Thai people," the princess told reporters.
Thai Equestrian Federation secretary-general Fuangvich Aniruth-Deva said the princess had done a very good job.
"The princess is already gifted but lacks the experience in competition," Col Fuangvich said.
The princess took up equestrianism seriously a few years ago after winning gold in the women's badminton team event at the 23rd SEA Games held in the Philippines in 2005.
Competitors in equestrian events at the current SEA Games in Myanmar have not been allowed to bring their own horses for quarantine reasons. As a result, they were required to draw horses from a local pool prepared by the hosts.