Most of the casualties were caused by the bomber who walked into the restaurant with explosives strapped around his waist, Col. Ahmed Muse told The Associated Press.
Many of the wounded at Baidoa's main hospital had horrific injuries, nurse Mohamed Isaq told the AP.
The al-Qaida-linked al-Shabab extremist group claimed responsibility for the blasts via its radio arm, Andalus. It said one blast targeted a hotel owned by a former Somali minister, Mohamed Aden Fargeti, one of several candidates running for the presidency of the region in November's election.
Baidoa is a key economic center about 250 kilometers (155 miles) west of the capital, Mogadishu, and about the same distance east of the Ethiopian border. Al-Shabab, which controlled Baidoa between 2009 and 2012 before being driven out by Ethiopian-backed government forces, still holds parts of southern and central Somalia.
The blasts came a day before Somalia marks the first anniversary of the deadliest attack in its history, a truck bombing that killed more than 500 people in Mogadishu.
Attention in recent days has turned to Baidoa, the interim capital of South West state, as high-level al-Shabab defector Mukhtar Robow seeks the regional presidency in November.
On Saturday he visited some of the wounded in Baidoa's main hospital, condemning the attacks and calling on people to team up in fighting the extremist group of which he once was deputy leader.
Robow is the highest-ranking official to have ever quit al-Shabab, surrendering to the Somali government last year after the United States cancelled a $5 million reward offered for his capture.
Somalia's government earlier this month said Robow was not eligible to run for the regional presidency because he is still under U.S. sanctions that were imposed against him in 2008 when he was identified as a "specially designated global terrorist."
Robow, who has yet to respond to the government's statement, has continued his campaign and remains registered on the list of candidates.
He is among several people challenging former Somali parliament speaker and incumbent regional president Sharif Hassan Sheikh Aden. Among the candidates is Somalia's former intelligence chief Hussein Osman, who has just resigned.
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