One bomb exploded outside a convenience store near a school while a second bomb went off near a police station.
"The explosions were roughly seven minutes apart. Five people were injured at the convenience shop ... they are all responsive and have been sent to hospital. Nobody was injured in the second blast," said Krissada Boonrat, governor of Songkhla province where the city is located.
"We have blocked all important roads to the town and are doing checks of those who come and go."
Police said they suspected Muslim insurgents were responsible for Tuesday's attacks.
The three southern provinces are covered by a tough emergency decree that gives the military wide-ranging powers of search and arrest.
Hat Yai, an important trade hub 755 km (470 miles) from the capital, Bangkok, is not covered by that law. Suspected Muslim insurgents staged a series of car bombs in the town centre that killed 14 people and injured more than 300 in 2012.
More than 5,700 people have been killed in insurrection in the south since January 2004.
The opening of peace talks with rebel groups last year has done nothing to end the violence. The talks appear to have stalled while Thailand's caretaker government deals with six months of street protests aimed at toppling Prime Minister Yingluck Shinawatra.