The violence erupted during a stand-off between supporters and opponents of Prime Minister Yingluck Shinawatra.
The shots were fired as demonstrators blockaded a building where ballot papers are being stored, in an attempt to prevent their distribution.
There was no word on who was responsible for the gunfire. It is was also unclear whether those struck were government supporters or opponents.
Before the attack, protesters had attacked a car and set off a series of small bombs.