According to U.S. Customs and Border Protection (CBP), the unidentified boy died early Tuesday after showing "signs of potential illness" on Monday.
The boy, whose name has not yet been released, passed away just after midnight on December 25, Christmas Day, at Gerald Champion Regional Medical Center in Alamogordo, New Mexico.
"The child was initially diagnosed by hospital staff with a common cold, and when evaluated for release, hospital staff found a fever", the news release said.
But later that evening, he was vomiting and was sent back to the hospital.
CBP said on Tuesday that the Guatemalan boy's death is being reviewed by the agency's Office of Professional Responsibility, and that the Inspector General has been notified of the death. Officials said more information would be released shortly.
The child, one of 163 people to have handed themselves over to border officers, died of dehydration and shock in a hospital in El Paso, Texas. It was not clear where the boy was being held or when he was apprehended, and a CBP spokesman declined to provide additional details.
A seven-year-old Guatemalan girl died earlier this month after being apprehended by border agents. The body of the girl, Jakelin Caal, was returned to her family's remote village Monday for burial Tuesday.
Jakelin's family has disputed CBP reports that the child went several days without food and water before she died, saying she was healthy when she arrived in the United States.
Democratic members of Congress and immigration advocates sharply criticized CBP's handling of the death and questioned whether border agents could have prevented it by spotting symptoms of distress or calling for an evacuation by air ambulance sooner.
The death comes two weeks after another migrant child, Jakelin Caal Maquin, died after being detained by border agents.