Armed raiders set fire to houses overnight, a local official said.
"We heard gunshots and screams, then there was smoke all over," said Jillo Dabacha, according to Reuters news agency.
The raid happened in the Tana River area of Coast Province, where clashes between the Orma and Pokomo communities killed at least 52 people last month.
"These are revenge attacks," Kenya Red Cross official Nelly Muluka told the AFP news agency.
Local residents told the BBC that the attackers were wearing military uniforms and carrying "sophisticated weapons". They said five men, six women and a child had been killed.
"It was this morning at 6 o'clock when armed men in full gear of army clothes surrounded Chamwanamuna village and started shooting," Timson Maneno told the BBC's Focus on Africa programme.
"They surrounded the whole village so villagers could not go out anywhere - and when people started running here and there they started burning the houses."
He said police posted in the nearby village of Semikaro then arrived on the scene, shooting and creating a space for the villagers to escape.
Mohammed Morowa, a Pokomo, told the AP news agency that 11 of those killed were his relatives.
The BBC's Jamhuri Mwavyombo in Malindi, where injured villagers have been taken to hospital, says people are fleeing areas along the Tana River towards the coastal town fearing further attacks.
Chamwanamuna residents have been congregating at a primary school not far from the hospital, she says.
The Orma and Pokomo communities have a long history of tension over access to land and water.
The Pokomo are mostly farmers, while the Orma are semi-nomadic cattle-herders.
Some analysts say there may be a link between the violence and national elections which are due in March 2013.
Twelve people have been killed in renewed ethnic clashes in a remote part of south-eastern Kenya, officials say.