The device exploded as the bomber was denied entrance to Indian Ocean, a popular seaside restaurant, as another bomb exploded inside, police officer Abdi Yasin Hassan said.
Last month a bomb was set off in the same area, killing a security guard, CNN said.
The Somali Shabelle Media Network said such attacks are typically carried out by the militant group al-Shabaab, which linked to al-Qaida.
Al-Shabaab was forced out of Mogadishu in 2011 but is often found responsible for roadside bombings and suicide attacks.
Notable deaths of 2014 [PHOTOS]
2 extreme skiers die in Chile avalanche