More than 120,000 people have been displaced, Kenyan government says, with 22 others injured and eight reported missing.
President Hassan Sheikh Mohamud has called a meeting of regional leaders.
Rift comes after Somaliland deal giving landlocked Ethiopia access to the Red Sea.
Mogadishu also shuts down Addis Ababa’s consulates in Hargeisa, capital of the Somaliland, and Garowe in Puntland.