The Guatemalan infant was stopped by patrolmen for illegally crossing the Mexican border with her dad.
She died of septic shock after not taking water or food for several days, according to reports.
"Our sincerest condolences go out to the family of the child," CBP spokesman Andrew Meehan said in a statement.
"Border Patrol agents took every possible step to save the child's life under the most trying of circumstances. As fathers and mothers, brothers and sisters, we empathise with the loss of any child."
The little girl reportedly started having seizures over eight hours after being detained.
She was flown to hospital where she died.
Donald Trump has enforced hard-line immigration policies, and attracted particular criticism for separating immigrant children from their families.
He has repeatedly discussed building a wall across the US-Mexico border to stop movement of people.
Bidders have started building prototype walls, each of which will be 30ft long and 30ft tall.
Trump has sent 5,800 troops to "harden" the border, including with barbed wire,
Last month US border agents fired tear gas at a migrant caravan trying to sneak into the country from Mexico.
Tijuana Mayor Juan Manuel Gastelum declared a humanitarian crisis in his border city of 1.6 million, which he says is struggling to accommodate the crush of migrants.
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