Hundessa, 34, had received several death threats linked to the "political potency" of his songs, prior to his killing which has sparked protests in his home region.
Many of his fans believe, the reason for shooting him dead was politically motivated.
No arrest linked to the killing has been made, according to local rights activists.
Ahead of his burial flags in Oromia as flying at half-mast as the Ethiopian police crack down on protesters, making a series of arrest including of media personality Jawar Mohamed.
Violent clashes with the police in the towns of Adama and Chiro have led to the death of five people including one officer.