A car bomb exploded outside a restaurant as people were watching the English Premier League match between Manchester United and Arsenal.
In a second explosion, a suicide bomber blew himself up at a busy junction.
This is the fourth major al-Shabab attack in Somalia since the beginning of the year.
It came on the same day as countries which contribute to the African Union force in Somalia pledged “to reinforce military operations in Somalia, to effectively counter threats from al-Shabab”.
President Hassan Sheikh Mohamud held an emergency cabinet meeting on Sunday evening in response to the Baidoa attack, and Security Minister Abdirizak Mohamed Omar called for extra laws to help the government fight the militant group.
In addition to the 30 deaths, the attacks injured 60 people who are being treated in hospital, a local journalist told the BBC.