One of the officials said an unmanned drone launched the missile in the late evening hours, but declined to confirm the suspect's identity or whether the strike was successful.
The US government has "been tracking this guy for years," the official told AFP on condition of anonymity.
A second US official said the strike in the southeastern port town of Barawe "was against a senior Shebab commander."
"The US is assessing the results of the operation" to determine if the suspect was killed, the official added.
The US strike took place just a day after the Shebab, which are linked to al Qaeda, called for attacks against foreign forces.
Shebab insurgents control large parts of rural southern Somalia, and despite having been driven from a string of towns by the UN-backed mission known as AMISOM, guerrilla units stage regular deadly attacks in the capital Mogadishu.
The United States has sent a handful of military advisers to Somalia in recent months to help bolster an African Union force fighting militants there.
The deployment marked the first stationing of US troops in the troubled country since 1993, when two Blackhawk helicopters were shot down and 18 Americans were killed in a disastrous operation.
Top Shebab commanders, including Ahmed Abdi Godane, met this week after Ethiopia formally joined AMISOM, Shebab spokesman Ali Mohamud Rage told AFP.
Ethiopian troops moved into Somalia in 2006 in a US-backed invasion, but pulled out three years later in the face of stiff opposition. They formally crossed back into Somalia in November 2011, where units have remained ever since.
Ethiopia had sent troops into its lawless neighbor in a US-backed invasion in 2006, but the move sparked a bloody uprising and the troops pulled out three years later after failing to restore order.
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