The four were injured as they prepared a mosque for a visit by Crown Prince Vajiralongkorn.
Police in the southern town of Pattani said they suspected it was caused by militants.
More than 1,700 people have been killed since January 2004, when Islamist separatists began a violent campaign.
General Sonthi Boonyaratglin, the coup leader and the first Muslim to head the Thai army, was previously responsible for resolving the conflict.
He had offered to hold peace talks with separatist groups and there had been optimism that his conciliatory approach would produce results.
Thailand's new military rulers have drawn up a four-man shortlist for the country's next prime minister, military sources said on Saturday.
The list includes the former World Trade Organisation head, Supachai Panitchpakdi, the sources said.
Senior legal and banking officials also feature among the candidates and the list is to be sent to King Bhumibol Adulyadej on Wednesday to decide who will replace Thaksin Shinawatra following the coup, sources said.
On Friday, more than 100 protesters defied a ban on public gatherings and denounced the military overthrow of Thaksin, in the first anti-coup rally since he was deposed.
"Don't call this reform, this is a coup!" said one sign held by protesters, who stood scattered in several groups to avoid the restrictions banning public gatherings of more than five people.
The protest was heavily covered
by the Thai media
The coup leaders, meanwhile, appointed nine people to investigate alleged corruption under Thaksin's rule and said they would write a new constitution to make future leaders more accountable.
The revived National Counter Corruption Commission includes Klanarong Chanthik, who had been secretary-general of the body in 2001 when it unsuccessfully sought to prosecute Thaksin for concealing assets.