"At least 11 people -- most of them women and children -- were killed by a bomb placed in a busy market," said lawmaker Mohamed Ibrahim Habsade.
The attack was the worst in Baidoa since the town was wrested from Al-Qaeda allied Shebab insurgents by Ethiopian-backed Somali forces in February.
"Many more were injured in the explosion, which was biggest since we took control of the town," Habsade said.
Witnesses said the bomb was detonated after Somali government troops entered the market, but that the majority of those killed were civilians.
"This was a disaster," said Adan Hassan, a witness. "I saw several dead bodies of at least nine civilians, most of them women -- the explosion occurred as people were shopping."
"Around 35 people were injured, some of the seriously," said Abdirahman Waney, another witness.
Baidoa, located 250 kilometres (155 miles) northwest of Mogadishu, was the seat of Somalia's transitional parliament until the hardline Shebab captured it three years ago.
African Union troops deployed in the town last week, the first time the force has dispatched troops outside the capital Mogadishu since the 10,000-strong force was set up five years ago.
The AU Mission in Somalia (AMISOM) sent 100 Burundian and Ugandan soldiers to Baidoa following Ethiopia's capture of the town from the hardline Shebab.
No group immediately claimed responsibility for Monday's bombing, but the Shebab have launched a series of recent guerrilla attacks and vowed to topple the Western-backed government.
Last week, six people including two top Somali sports officials were killed in an attack on the newly reopened national theatre in Mogadishu by a female suicide bomber, narrowly missing the prime minister and seven other ministers.
A broad offensive by Ethiopian and Kenyan forces in southern and western Somalia has forced the rebels from many of their strongholds, while AU troops in Mogadishu have advanced on to the outskirts of the city.
Despite the losses, the Shebab -- Somalia's most brutal militia -- remain a serious threat to internationally backed efforts to restore stability in the Horn of African country plagued by a devastating civil war since 1991.
The absence of an effective government in Somalia since it plunged into a civil war two decades ago has allowed armed groups, pirate gangs and extremist militia to carve up the country into mini fiefdoms.
Although the Shebab have lost ground recently, analysts warn that they still remain a serious threat to efforts to restore stability in Somalia.
Since abandoning fixed positions in Mogadishu in August, the Shebab have been chased out of most of their strongholds, with the notable exception of the southern port of Kismayo, switching instead to guerrilla attacks.
