A car bomb detonated outside The Village blew much of the roof off the building, the BBC reported.
A suicide bomber then mingled among the crowd that gathered and set off an explosive vest, local reports said.
Shabelle Media Network, based in Mogadishu, said the second blast -- which the agency reported as another car bomb -- targeted security forces attempting to secure the area and assist the injured.
No group has yet claimed responsibility for the blast.
The restaurant, about a half mile from the parliament, is outside the city's security zone. It also was targeted in September 2012 by two suicide bombers who killed 14 people.