Members of the militant group Hizbul Islam confirmed the arrests to reporters Monday and warned people not to watch the matches, which they called a waste of time.
Hizbul Islam arrested at least 14 people late Sunday after raiding a home in the town of Afgoye where people were viewing the match between Germany and Australia.
Hizbul Islam and another Islamist group, al-Shabab, control large parts of Somalia after a three-year battle against the United Nations-backed transitional government.
Both groups have moved to impose a harsh form of sharia, or Islamic law, in the areas under their rule. In April, Hizbul Islam banned Mogadishu radio stations from playing music, saying it was un-Islamic.
Witnesses in Somalia say hardline Islamists have arrested more than a dozen people for watching the World Cup on television.