Security sources said four armed men threw a grenade at a small shop in the town center on Tuesday night. They also opened fire before escaping on foot.
Local police said the shop caught fire, burning the bodies of the victims beyond recognition, AFP reported.
"It is barbaric to say the least," said a senior police officer who asked not to be named. He said three people were killed and three wounded.
Somalia's Shebab militants claimed responsibility for the attack.
"We attacked Wajir and killed four. Such attacks will continue," said Abdulaziz Abu Musab, a spokesman for the al-Qaida-affiliated militants.
The attack in Wajir is the fourth in five days in Kenya's remote and increasingly lawless northeast, which borders Somalia.
On Friday the convoy of the governor of Mandera, Ali Roba, was ambushed. Gunmen carried out a drive-by shooting in Mandera town on Sunday and on Monday a bomb was detonated at a nearby border post.
The recent string of attacks has so far claimed at least seven lives. On Monday Roba said the security situation in northeast Kenya was "extremely hopeless".
Shebab has threatened to continue its attacks until Kenya pulls its soldiers out of Somalia where they are part of an African Union mission aimed at defeating the insurgents and protecting the internationally backed government in Mogadishu.