A witness told VOA Somali Service that a thermos filled with explosives was placed in a local market and was detonated Monday afternoon.
The regional governor, Abdifatah Mohamed Gesey, told VOA that "more than 10" people were killed but the figure is not final.
He said that two people have been arrested for the attack.
"Our troops on patrol have arrested a man who carried the ice thermos into the market and another man who may have had the remote detonator," said Gesey. "They will be put on trial."
There was no immediate claim of responsibility for the bombing.
African Union troops deployed to Baidoa last week, a few weeks after Ethiopian troops backing the Somali government captured the town from militant group al-Shabab.
Al-Shabab has lost large amounts of territory to AU, Ethiopian, and Kenyan forces in the past year but continues to carry out bombings and suicide attacks.
The group claimed responsibility for the bombing of Somalia's newly-reopened National Theater in Mogadishu last week. That blast killed at least seven people, including the heads of Somalia's Olympic committee and football federation.