The bombing occurred in front of the Pithan Panich Company and a tea shop around 7am.
The victims were identified as retired Pol Sen Sgt Maj Chamras Thongkase, Pol Sen Sgt Maj Veera Kongkaew, who had taken early retirement from the police, and Sompob Saowaneepithak.
The initial investigation revealed that two teenagers entered the tea shop before the blast.
The explosion from a home-made bomb was detonated by a mobile phone signal and caused a 30cm hole in the floor.
The attack in Songkhla was the first in several months.
Defence Minister Sukumpol is on a monthly visit to Narathiwat to inspect security operations in the insurgency-torn region. He was briefed by the Fourth Army Region commander on the situation.
He admitted that it is difficult for military operations to cover the entire region due to complications of the conflict and said that time is needed to solve the problems.
The Friday visit came as the defence minister is reportedly about to be removed from his post. Prime Minister Yingluck Shinawatra is widely tipped to take the defence portfolio in her fifth cabinet reshuffle.
Elsewhere, army rangers clashed with suspected insurgents in Rueso district during their raid in a house believed to be the hideout of the group.
They exchanged gunfire for about 15 minutes. One ranger was injured in the clash. Seven suspects were arrested with .38 pistols. They were taken to Narathiwat for further investigation.