The boy, identified by Guatemalan authorities as Felipe Gómez Alonzo, had been in CBP's custody with his father, Agustin Gomez, since Dec. 18.
CBP said in a statement late Tuesday that an agent first noticed the boy had a cough and "glossy eyes" at about 9 a.m. Monday.
He was eventually hospitalized twice and died just before midnight, the agency said.
CBP earlier said that the boy died just after midnight.
A CBP spokesman could not immediately answer how many children are currently in the agency's custody.
But with border crossings surging, CBP processes thousands of children — both alone and with their parents — every month.
The body of 7-year-old Jakelin Caal , who died earlier this month, was returned this week to her village in Guatemala for burial. »