The long-time member of the Federal Parliament was reportedly ambushed by gunmen at Karan District on the eastern flank of the Somali capital.
Initial reports indicated that some of the men involved in the assault were apprehended and their saloon car detained by security forces, though the claims could not be independently verified.
Mr Boqore becomes the first MP killed in Somalia this year.
Members of the Federal Parliament are often a prime target of the jihadists, who were seeking to establish an Islamic state in the Horn of Africa.
Mr Boqore previously served in the legislative House that was formed in a Nairobi suburb in the Kenyan capital, following a two years reconciliation conference for various Somali groups.
Prior to his killing, he was a member of the Parliamentary Defence Committee.
President Mohamed Abdullahi Farmajo, who is currently attending the Arab-European Summit at Sharm El Sheikh, Egypt, ordered an enquiry into the killing of the MP.
Somalia has struggled to establish a central authority and return to stability since the fall of dictator Siad Barre in 1991.
Some regions have since seceded but failed to win international recognition, while the Al-Shabaab control large swathes outside the Mogadishu and African Union (Amisom) peacekeepers' control.