Police spokesman Sadiq Ali Adan blamed the attack on the local al-Shabab extremist group, DW reported.
The explosion occurred at dinner time when the restaurant was full. The blast reportedly could be heard across the city.
In addition to the restaurant, several nearby buildings were also damaged and at least one collapsed after the bombing.
This is the second time the Luul-Yemeni restaurant, which is popular with city workers, government employees and security personnel, has been attacked.
The Luul Yamani restaurant also was attacked last year.
Security in Mogadishu had been especially heavy, with thousands of government forces deployed in anticipation of a planned demonstration on Saturday by an alliance of opposition leaders over the country's delayed national election.
Authorities blamed the attack on the al-Shabab terrorist group.
The group is linked to al-Qaeda and frequently carries out attacks against targets like hotels and restaurants in the city of Mogadishu.
For years, the group has been carrying out bombings as part of its bid to topple the central government in Somalia, located in the Horn of Africa.
Al-Shabab currently controls large parts of the country's south and center.