On February 2, Shebab "mujahideen carried out an operation targeting dozens of Western intelligence officials and Turkish NATO forces aboard an airplane bound for Djibouti," said a statement issued by the group.
It is the first time the Al-Qaeda-affiliated Shebab have claimed an attack against an airliner and shows the group was able to get around the heavy security at Mogadishu's airport, if it was indeed responsible for the bombing.
The Shebab said the attack was "retribution for the crimes committed by the coalition of Western crusaders and their intelligence agencies against the Muslims of Somalia."
Two of the 74 passengers aboard were slightly injured.
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A passenger believed to be the bomber, identified as Abdulahi Abdisalam, was killed, probably after being propelled out of the aircraft in the explosion, investigators said.
The man had initially intended to board a Turkish Airlines flight but the Turkish plane did not turn up and Daallo Airlines agreed to fly the passengers onwards to Djibouti.
Somali intelligence officials have released surveillance footage appearing to show a passenger being given a laptop in which the bomb was concealed.
Turkish Airlines is one of the only major international airlines to fly regularly to Mogadishu.
The city's airport is heavily fortified and adjoins the capital's main base of the African Union mission to Somalia, the 22,000-strong force backing the government in the battle against Islamist Shebab insurgents.
According to several aeronautics experts, the explosion was not more deadly because it happened at a low altitude shortly after take off, when the cabin had not yet been pressurised.
"This validates the procedure -- when there are suspicions of a bomb aboard -- to descend to an altitude where the air is breathable... Before landing the plane as quickly as possible," airplane security expert Xavier Tytleman told AFP previously.