Several other people were also hospitalised, some of them after being beaten with clubs by security forces in a crackdown following the killing of three soldiers in Garissa, a garrison town near the border with war-torn Somalia.
The violence is separate from riots that shook the capital Nairobi on Monday, although both broke out following attacks that resembled a recent string of grenade blasts and shootings blamed on supporters of Somalia's al-Qaeda-linked al-Shebab insurgents.
"This morning, Kenya Red Cross rescued four males, four females and two children, eight of them being gunshot casualties," the local Red Cross said in a statement, adding that 34 other casualties were taken to Garissa hospital.
Musa Mohamed, a doctor at the hospital, said that "at least 15 people were admitted this morning with various injuries".
Garissa's main market was torched during the violence that broke out Monday, after unknown gunmen killed three soldiers in town, sparking a security crackdown that provoked violent protests.
Small scuffles were also reported on Tuesday in Nairobi's Eastleigh district, a predominantly ethnic Somali neighbourhood, but on a far smaller scale than on Monday, when street battles took place the day after a bomb blast on a bus killed nine people.
Senior al-Shebab official Abduaziz Abu Musab denied involvement in Sunday's bomb blast in Nairobi, but said it was possible "some sympathisers of our cause acted alone" in the shooting of the soldiers in Garissa.
"We are categorically denying any involvement in the bus attack in Eastleigh at the weekend," Musab told AFP, blaming the violence on Kenya's elections due in March 2013.
"The violence is instead related to the upcoming election in Kenya and was masterminded to harm the Muslims in Kenya," he told AFP.
The al-Shebab have vowed revenge after Kenya invaded southern Somalia last year to chase out the Islamist fighters, although the group has not claimed direct responsibility for any attack.
Violence in Kenya – ranging from attacks blamed on Islamists to inter-communal clashes to a police crackdown on a coastal separatist movement – have raised concerns over security ahead of next year's elections.
Five years ago, elections descended into deadly post-poll killings that shattered Kenya's image as a beacon of regional stability. – Sapa-AFP