Police said a car bomb exploded outside the Banadir Beach Club in the Lido area and gunmen then stormed the building.
Security forces say they killed two attackers and arrested another after a six-hour operation overnight.
The militant Islamist group al-Shabab stages regular attacks in Mogadishu and other parts of Somalia.
Earlier this year, 17 people died when the group stormed a restaurant on Lido beach.
Al-Shabab, which is linked to al-Qaeda, was ousted from Mogadishu in August 2011 but still has a presence in large areas of southern Somalia.
