"The official number of the dead has reached 30 people - all of them civilians - and 61 others have been wounded, 15 of them seriously," Abdurashid Abdulahi, governor of Bay region, told AFP.
An initial car bomb struck a popular restaurant in a busy part of the regional capital yesterday afternoon, with a suicide bomber nearby hitting people as they fled the area.
"The explosion occurred in a densely populated area," said Abdirahman Ibrahim, a police officer in Baidoa.
The explosions shredded the roofs of nearby buildings, tore chunks out of vehicles and left bodies, plastic chairs and tables strewn across the road.
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The Al-Qaeda aligned Shebab jihadists claimed responsiblity for the attacks, saying local officials were targeted.
"The mujahideen carried out two massive explosions in Baidoa targeting restaurants used by members of the apostate South West Administration," the Shebab said in a statement.
The regional administration in Baidoa is protected by troops of the 22,000-strong African Union Mission in Somalia (AMISOM), which is protecting the internationally-backed government of Somalia.
On Friday Shebab gunmen stormed a hotel in the capital Mogadishu and bombed a nearby park killing at least 14 people and wounding 18.