According to Somalia's information ministry, a U.S. Navy Seal was also killed and two troops wounded in the Friday raid on an al Shabaab militant compound.
Senior Chief Special Warfare Operator Kyle Milliken, 38, was a distinguished 15-year veteran who had had been awarded the Bronze star for heroism in combat four times.
The U.S. Africa Command, responsible for all American military operations on the continent, said forces came under attack during an advise-and-assist mission alongside members of the Somali National Army.
"Senior Chief Kyle Milliken embodied the warrior spirit and toughness infused in our very best Navy SEALs", Rear Admiral Timothy Szymanski, Commander, Naval Special Warfare Command, said.
It goes on to say, "He was a devoted father and son, a true professional and a wonderful husband".
According to the Pentagon, Milliken was on assignment with the the East Coast-based special warfare unit in a remote area 40 miles west of Mogadishu.
The Pentagon called it the first U.S. combat death in Somalia since 1993, when USA forces pulled out of the African country in the wake of the "Black Hawk Down" incident, in which two helicopters were shot down and bodies of American soldiers were dragged through the streets.
A regional leader of the al-Shabab extremist group has been killed in a raid by Somalia's military, the government announced Sunday, as the country's new offensive against the fighters moves ahead.
The other injured service members are receiving proper medical attention and were taken to neighboring Djibouti for care.
U.S. Africa Command has provided intelligence, training and logistical support to the Somali army and to African Union troops battling Shabab since 2013.
Two other military service members were wounded in the operation, including an interpreter who was also a U.S. citizen, a USA defense official told CNN.
Former President Barack Obama had increased USA military presence in Somalia during the final months of his final term in office.
"Al-Shabab presents a threat to Americans and American interests", U.S. Africa Command said in a statement on Friday. The mission was not part of the stepped-up effort in Somalia to conduct airstrikes and ground missions against terror targets.