The bombs detonated at around 8.20 pm local time in Songkhla province's Hat Yai city, said Lieutenant General Ongkorn Thongprasom, the regional army commander.
Several people were reported wounded in the attacks and were sent to nearby hospitals.
Local television pictures showed images of bloodied victims lying in restaurants or being led to safety by rescue workers.
There were reports that up to five people had died but these could not be confirmed.
One of the dead was a Western tourist, reportedly a Canadian citizen, police sources said.
Security forces have cordoned off the areas around the bomb sites and jammed mobile phone transmissions to prevent further blasts, police said.
The Hat Yai city is the largest in the country's south and is popular with Singaporean and Malaysian tourists who do their shopping there.
Military authorities blamed Islamic separatist insurgents for the attack.
A military spokesman told AP news agency: "We do believe that the insurgents are responsible for the attacks.
"Their intention is to spread fear in the region."
Parts of Songkhla province are under martial law as the Thailand government attempts to quash an Islamic insurgency that has killed more than 1,400 people since 2004.