The operation took place about 185 miles southwest of Mogadishu and was carried out in coordination with USA regional partners as a "direct response" to the actions of al-Shabab, which include recent attacks on Somali forces, according to the Pentagon.
In March, the southern portion of Somalia was temporarily designated by Trump as an "active area of hostilities" for 180 days, according to a US official.
The US attack was carried out by at least one armed Reaper drone flying from a base in Djibouti, a US official said.
In a statement, Somali President Mohamed Abdullahi Farmajo said he authorized the dawn strike on the militants training base near Sakow which Al-Shabab used as command and supply hub. As a result, al-Shabab also has increased its military strength by seizing armored vehicles, heavy weaponry, explosives, small arms, ammunition and other supplies, the command said.
Somalia's president said the country's army was in "hot pursuit" of the fighters after the attack.
The U.S. military has confirmed its special forces killed eight Al-Shabaab militants during a successful airstrike conducted in southern Somalia on Sunday.
The Al-Qaeda affiliated group is fighting to overthrow the Somali government and establish Islamic law.
Somalia has been a scene of deadly clashes between government forces and al-Shabaab militants since 2006.
But it still retains a strong presence in swathes of the south and center and still carries out major gun and bomb attacks.
US officials won't say precisely how many American troops are in Somalia now.
It appeared to be the first United States military death in combat there since the infamous events of "Black Hawk Down" 24 years ago, when 18 American servicemen died in what is now called the Battle of Mogadishu.
"For those who have suffered under Al-Shabaab, and for the rest of Somalia, I want you to know that we are committed to defeating Al-Shabaab and uniting our people", Farmajo stressed.