The transitional cabinet also named an attorney-general and the man who will run the day-to-day affairs of the central bank, government spokesman Abdirahman Dinari said on Wednesday.
The transitional government, however, has no functioning army, central bank or justice services. They will all have to be set up once the government returns to Somalia from Kenya, officials said.
Somali leaders are based in neighbouring Kenya because the anarchic Somali capital of Mogadishu is considered unsafe.
The appointments, made during a cabinet meeting on Tuesday, triggered public protest from some ministers and members of the transitional parliament who are visiting Mogadishu in an effort to create conditions that would encourage the government to relocate there.
Fighting in Somalia has displaced
many to neighbouring countries
The appointments were made without full consultation with key members of the cabinet, said Security Minister Muhammad Kanyare Afrah.
The dispute highlights a deepening rift between members of the government led by transitional President Abd Allah Yusuf Ahmad.
Somalia has been without a central government since clan-based warlords overthrew Muhammad Siad Barri in 1991. Leaders of armed factions then turned on each other, sinking the nation of 7 million into anarchy and creating a refugee crisis in neighbouring countries.
A new transitional government was formed last year to bring peace to Somalia. But it only named the first key civil servants on Tuesday, appointing General Ismail Qasim Naji as the new army chief.
The cabinet also named Abd Allah Dahir Barri, a lawyer and former head of a regional court, as the attorney-general.
Former banker Bashir Isa Ali was named director general of the central bank.
The cabinet also named a 13-member commission to determine how to transform Somalia's government into a federal one.