Regional governor Abdikadir Mohamed Nur told Reuters that members of the Somali terror group had fired on the drone for several hours before the unmanned aircraft went down.
For their part, the group admitted a U.S. unmanned aircraft had crash-landed in southern Somalia.
However, the terror group did not say whether its members shot down the surveillance drone.
The reported shoot down comes as the White House is preparing to ramp back its aggressive use of armed drone operations across the globe.
In his national security speech last Thursday, Obama defended U.S. drone strikes abroad, saying that they were legal and necessary in the fight against terrorists.
But he also expressed caution about using drone strikes as he discussed the importance of seeing the U.S. war on terror come to a close.
“To say a military tactic is legal, or even effective, is not to say it is wise or moral in every instance,” Obama said in his speech at National Defense University. “For the same human progress that gives us the technology to strike half a world away also demands the discipline to constrain that power — or risk abusing it.”
American and allied forces have surged unmanned assets, both for surveillance and for targeted airstrikes against suspected terrorists, into Africa for the past several years.
Drone operations on the continent have been focused on al Shabaab in Somalia, as well as the militant group Boko Haram and al Qaeda's West Africa cell, known as al Qaeda in the Islamic Magreb (AQIM).
The Pentagon's newest counterterrorism outpost in Niger went operational in March, providing a new launching pad for U.S. officials to carry out surveillance and armed drone strikes against AQIM and their affiliates in western Africa.
Along with the drone base in Niamey, Niger, U.S. officials also carry out unmanned intelligence and airstrike operations from Camp Lemonnier in Djibouti, as well as a clandestine base in Ethiopia and the Seychelles, according to recent reports.
Unmanned U.S. and allied aircraft were reportedly used to support the March 2011 NATO peacekeeping mission to oust former Libyan dictator Moammar Gadhafi
Gadhafi's forces reportedly were able to shoot down a Navy Scan Eagle surveillance drone during that NATO mission in Libya.
American drones were also used to collect intelligence and conduct surveillance operations during the French-led counterterrorism mission to push AQIM fighters from their strongholds in northern Mali earlier this year.