The group started their protest after they were banned from watching the semi final between Germany and Italy by Islamists.
The militia loyal to Somalia’s Sharia courts fired first into the air to break up the crowd before firing on them when the protest increased.
"They closed the hall and forced viewers to go home but this angered everybody and prompted a demonstration," one witness told AFP on condition of anonymity.
Those killed included cinema owner Mohamed Hirsi Dhore and a young girl Sahro Ondhoweyne.
"They said they will not allow any cinema to operate," another witness said.
The Islamists who seized several provincial towns from US-backed warlords have been enforcing Sharia law which includes a ban on cinema and television.
At least two people were killed last month during similar protests.
World Cup broadcasts have drawn criticism from clerics who view some elements of the broadcast, particularly advertisements for alcohol, as evil.
The ban had been previously repealed after the first fatal shootings and residents had been allowed to watch the World Cup in some areas of the city.
The Islamic courts had first closed down cinema halls showing Hollywood and Bollywood films last year claiming they were contravention of the strict interpretation of Islam.