Eyewitnesses said one attack took place at a junction and the other at a restaurant.
Abdulfettah Ibrahim Hashim, head of Baidoa state hospital, confirmed the death and injury toll.
Some of the injured remain in critical condition and are being transported to Mogadishu, Hashim said, adding that the dead toll could rise.
Al -Shabaab militant group later claimed the attacks in a statement on Radio Andalus website.
Anadolu Agency