The number and identities of the bodies in the graves are unknown, police say. A court order to exhume the bodies has been requested.
More than 100 people have been killed in clashes in the area in the past month between farmers and cattle herders over land and water.
There are accusations that politicians have incited the violence ahead of elections next March.
The long-running conflict is between the Pokomo people - mostly farmers growing cash crops by the Tana River - and the Orma, semi-nomadic cattle herders.
But investors, both Kenyan and foreign, have been acquiring leases on vast tracts of land in the region for the purposes of large-scale cultivation of food and biofuel crops, says the BBC's Gabriel Gatehouse in Kenya.
Getting elected to office can mean gaining control of such lucrative deals, our correspondent says.