A number of arson attacks and blasts also took place Pattani province, one of which temporarily cut the provincial capital's electricity.
Two villagers in Pattani were also shot dead in an ambush Sunday night.
More than 1,900 people have been killed in Thailand's Muslim-majority south since the latest separatist campaign began in January 2004.
Sunday's attacks hit as Thailand was celebrating the Lunar New Year.
"There are efforts to create chaos and make the news worldwide," Colonel Acar Tiproch, the national army spokesman, said.
"They use the festival time to show that there is not peace in the three provinces in the south."
He said the army now had control of the situation.
The bombings across the three troubled provinces began at about 7pm local time (1200 GMT).
Karaoke bars hit
In Yala town, police said nine blasts hit karaoke bars, petrol stations, hotels, a golf course and a cinema, while in a remote area of the province one person was killed in one of six blasts.
Panu Uthairat, Pattani's governor, told Thai television that three blasts there had hit the power plant.
A blackout ensued in Pattani town, but he reassured residents that 95 per cent of the supply had been restored.
In Narathiwat, seven bombings - the majority of which hit karaoke bars - started at 7:30pm, police said, killing one.
Fighters in Narathiwat also set fire to a central mosque and two schools.
School set afire
In Yala, a primary school was set alight. Teachers and schools are frequently targeted because fighters view them as symbols of Bangkok's effort to impose Buddhist Thai culture on the region.
"The militants show of force is trying to challenge the power of the authorities," Nithon Naratitakkul, Narathiwat's deputy governor, said.
"The pattern of the attacks is orchestrated across the three provinces, and they attacked at almost exactly the same time."
Police advised people in the three southern provinces to stay at home.
Violence along Thailand's southern border with Malaysia has surged since the military seized power in Bangkok in a bloodless coup in September, despite a raft of peace measures introduced by Surayud Chulanont, the army-installed premier.
In the latest gesture, Thailand said on Friday that it was willing to hold talks with separatists in the south with the help of neighbouring Malaysia, reversing an earlier statement denying such plans.
The three Muslim-majority provinces were once an autonomous sultanate, until the region was annexed by Thailand a century ago.
Separatist unrest has erupted periodically ever since.