The blast in the border town of Sungai Kolok in Narathiwat province came just hours after Prime Minister Thaksin Shinawatra met his security advisers amid fears of Muslim outrage over the protesters' deaths.
A preliminary report indicated 78 Muslim protesters suffocated to death when they were crammed into army trucks and driven five hours to a military barracks after being arrested during the protest.
Seven others were shot dead by Thai security forces.
Hospital sources said at least one person was killed and about 20 others were injured by the blast on Thursday. Many of the victims were in and around a bar in the tourist centre of the town, near a police station.
It was the same province where the 85 died on Monday.
"The bandit left a small plastic container behind the police station. We think it was a time bomb," Lieutenant General Thanee Twidsi, deputy commissioner for southern police, said.
Muslim leaders have warned of a violent backlash to Monday's tragedy.
"We will tell everything, every detail without hiding anything"
Prime Minister Thaksin Shinawatra
Thaksin, under pressure from close ally the United States to fully investigate the deaths, said the government's preliminary investigation into the incident will be announced on Friday.
"We will tell everything, every detail without hiding anything," Thaksin told reporters after the meeting with top generals and other security officials in Bangkok.