"A special battalion for assassinations targeted the district commissioner of Afgooye [Ali Adow] and two of his body guards," a group official was quoted as saying by the al-Shabaab-affiliated website Somali Memo.
The militant leader said that Adow was "tightening the noose around the Afgooye residents."
Earlier Monday, Adow was killed along with two of his guards when his car struck a landmine in Mogadishu, eyewitnesses and security sources have said.
The same explosion – which was followed by gunfire – left two passersby injured, one of the sources said.
Somalia has remained in the grip of on-again, off-again violence since the outbreak of civil war in 1991.