US Central Command (Centcom) said in a statement the casualties were caused by a drone attack at a base in northeast Jordan, near the Syria border.
US President Joe Biden said that the attack was carried out by "radical Iran-backed militant groups".
This is the first time US soldiers have been killed in the region after Hamas's 7 October attack on Israel.
There have been attacks on US bases in the region but so far there have been no casualties reported by the US army.
The White House said Mr Biden was briefed Sunday morning on the attack by US Defense Secretary Lloyd Austin and other officials.
"While we are still gathering the facts of this attack, we know it was carried out by radical Iran-backed militant groups operating in Syria and Iraq," Mr Biden said in a statement.
