The border agency says the boy died on Monday night hours after showing signs of illness. A Texas congressman named him as Felipe Alónzo-Gomez.
The child was detained with his father on 18 December after illegally crossing the US-Mexico border.
A seven-year-old girl died earlier this month just hours after being detained.
Jakelin Caal, also from Guatemala, developed a high fever and died of liver failure. Her funeral was held in her village on Tuesday.
Thousands of migrants have travelled from Central America - mainly from Guatemala, Honduras and El Salvador - to the US border.
Many say there are fleeing persecution, poverty and violence in their home countries and plan to seek asylum in the US.
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