The first blast was caused by a car filled with explosives that was detonated in a busy street near Baidoa Hotel and other business centers. Minutes later a suicide bomber detonated explosives in a busy restaurant.
Among the dead is Nur Malaq, Deputy Minister for Disarmament for the Southwest Regional Administration.
Militant group al-Shabab claimed responsibility for the blasts.
The blasts come just two days after two massive explosions claimed by al-Shabab killed 25 people in the capital Mogadishu and wounded nearly 60 others.
Al-Shabab, which has links to Al-Qaida, carries out frequent attacks in Somalia, often targeting government officials and African Union troops.
The Islamist militant group controlled most of southern Somalia as recently as 2010 but was pushed into the countryside by AU and Somali government forces.