Three Katyusha rockets were fired from a warehouse in Aqaba close to the port, a Jordanian government statement said. The warehouse had been rented a few days ago by four people of Iraqi and Egyptian descent.
The casualties occurred when one rocket flew over the bow of the USS Ashland and struck a warehouse used by the Jordanian military, officials said.
A second missile landed near a military hospital in Aqaba, and the third landed in the neighboring Israeli Red Sea port city of Eliat, the Jordanian government said.
The third rocket partially exploded, Israeli military sources said, damaging a road and a car. It fell on a road just east of the city's airport. No injuries were reported.
Israeli Defense Minister Shaul Mofaz said the two countries were cooperating in the investigation.
The ships were in port so sailors could train with regional partners, U.S. Navy Commander Jeff Breslau told CNN. "It's very unusual for U.S. ships to be under attack in this part of the region."