He is the second Guatemalan child to die in CBP jail this month.
The boy, who was imprisoned with his father, died shortly after midnight at the Gerald Champion Regional Medical Center in Alamogordo, New Mexico, about 90 miles north of the border crossing in El Paso, Texas.
He was taken to hospital on Monday after a border guard detected signs of illness. For the first time he was diagnosed with a cold and later diagnosed with a fever.
"The child was held for another 90 minutes for observation and then discharged from the hospital on prescriptions for amoxicillin and ibuprofen on mid-afternoon on December 24," CBP said in a press release.
Amoxicillin is a commonly prescribed antibiotic.
On Monday night, the boy began to vomit and was taken to the hospital for examination. He died hours later, the CBP said.
The official cause of death is unknown. CBP is reviewing and will post more details as they become available.
The Guatemalan government has been informed and has contact with the father and family members in Guatemala, CBP said.
The CBP press release states that the Department of Homeland Security "experiences a dramatic increase in unaccompanied children and family units arriving illegally or unauthorized at our borders." By law, they will release such persons until their deportation or in federal agencies to the United States with an announcement in court.
"During their imprisonment, they received medical examinations and other treatments as needed," it says.
A seven-year-old girl, Jakelin Caal Maquin, fled Guatemala with his father. After surviving the 2,000-mile journey to New Mexico, she died on December 8, less than 48 hours after CBP detained her and her father.
Her body was returned to Guatemala on Sunday, and her remains were to be transported to the indigenous community of Raxruha, where she called home to enforce immigration, and many of them ̵
Joe Sterling and Geneva Sands of CNN contributed to this report.