The sailor, who was not identified, was assigned to the Arleigh Burke-class destroyer Jason Dunham, which has been deployed from its homeport of Norfolk since the end of May. It has been operating in waters surrounding the Middle East in recent days.
The sailor had been conducting unspecified small boat operations in the Red Sea on Sunday when the injuries were sustained, officials said in news releases.
"The sailor was medically evacuated to a hospital in Aqaba, Jordan, and was pronounced dead at 12:45 p.m. local time," officials said in a release.
The circumstances surrounding the sailor's death are being investigated, officials said.
Defense Department policy dictates that names of deceased troops are not made public until 24 hours after next-of-kin are notified.
The Dunham, which is set to operate with the Harry S. Truman carrier strike group while deployed, conducted a passing exercise with elements of the Egyptian Navy earlier this month.
The destroyer's deployment is in support of operations to ensure maritime stability and security in the region, including three strategic choke points, according to Navy officials.