Speaking to Radio al Andulus al-Shebab spokesperson Sheikh Ali Mohamud Rageh said their fighters were behind the attack in which three people were killed and more than 15 others injured.
Rageh added that the target was senior members of Western officials, especially French commandos who frequent the restaurant.
“The attack was carried out against the French crusaders for involvement in the killings of our Muslim brothers in the Central African Republic and for their active role in training and equiping the apostate Djiboutian troops in Somalia and their growing intervention in the affairs of our Muslim lands,” he declared.
“Our mujahedin fighters say no to French crusaders, you cannot enjoy yourselves in our country and rip off resources and that attack was a payback to what you did to our brothers everywhere in this world”.
He also sent a strong message to Djibouti's president.
“We say to Ismail Omar Guelleh, you made it clear that you will fight against us and we say you are fighting Islam and we will defeat you”.
Rageh also said that al-Shebab will not stop its attacks until the Djiboutian government shuts the United States' main Africa base and expels from its territory key Western allies, including French forces.
French officers were among the casualties, he said.
“Our martyrs also targeted two senior French commanders who were at the restaurant during the attack, they inflicted them heavy casualties,” he said.
Djibouti troops are part of the African Amisom force that aims to drive al-Shebab from the southern and central regions of Somalia.
The twin bomb attacks targeted a restaurant known to cater for tourists and Western security officers.
They killed several people, including the two suicide bombers, said to have been a man and a woman.
Al-Shebab fighters have previously carried out attacks in Uganda and Kenya, which also contribute troops.