Men in two pickup trucks fired weapons and lobbed grenades Saturday into a noodle shop and then the People's Democratic Reform Committee rally in Trat, about 180 miles east of Bangkok, the Bangkok Post reported.
A PDRC spokesman said about 2,000 protesters were listening to speakers on a stage in a large market next to the shop at 9:30 p.m. when the trucks drove by.
One truck attacked the noodle shop where PDRC security guards were sitting and the other truck turned its weapons on the outdoor rally, the Post reported.
The girl reportedly was standing next to a food stall when she was shot.
"This attack was carried out by people who disagree with the PDRC in what was clearly a well-organized strike using M16s and grenades," PDRC spokesman Akanat Promphan said.
"The reason for the continued attacks on our rally sites is because the government is doing nothing to prevent them and has failed to find anyone culpable for past violence," he said.
Promphan said the attacks strengthen the anti-government movement and other protesters will join as a result.
The Nation newspaper reported Trat Gov. Benjawan Anplueng Sunday declared the Khao Saming market area a "disaster zone affected by terrorism."
The provincial government will speed up compensation payments to the injured people and the family of the slain child, she said.
Injured victims will receive about $76 in compensation and dead girl's family will get about $770.
The Trat attack is the latest violence against the PDRC's anti-government protest rallies, mostly in Bangkok.
At least four people, including policeman, were killed and dozens injured last week when Thai police tried to clear a large protest site in the capital occupied since the autumn, the BBC reported.
Violence escalated during the operation and police alleged they were targeted by snipers. Several police officers were seriously injured by a grenade reportedly thrown by protesters.
Police fired live rounds during the operation and arrested 200 protesters, the BBC reported.
The PDRC, led by Suthep Thuagsuban, a former opposition Democrat Party member, boycotted Feb. 2 national elections, which were won by the incumbent Yingluck Shinawatra and her Pheu Thai party.
But Shinawatra leads a caretaker government until April 20 and 27 when polling in parts of Bangkok and in nine provinces in the southern region can take place.
Some polling stations were unable to open and voters were unable to cast their ballots in early February because of alleged intimidation.
Yingluck unseated the Democrat Party in elections in 2011, but her administration has been crippled by accusations of corruption.
Her critics also allege she is a surrogate leader for her disgraced brother Thaksin. He was ousted in a bloodless military coup in 2006 that left the country divided.