The death marks the sixth known case in the last year, Al-Jazeera reported.
The US Department of Health and Human Services (HHS) announced that she died in late September at an Omaha, Nebraska, hospital, of fever and respiratory distress.
Spokesman Mark Weber stated that the department began caring for the unidentified girl in March 2018, adding that the girl was "medically fragile", with a history of congenital heart defects.
He did not say when she entered the United States or whether a parent or adult accompanied her. HHS provides care to children the government considers unaccompanied.
The deaths of immigrant children in US government custody have sparked calls for investigations and changes to the Donald Trump administration's policy.
Weber stressed that the department was committed to protecting the children in its custody.
The five other children who have died after being apprehended by the Border Patrol were from Guatemala, which is ravaged by violence, poverty and drought.
More than 114,000 people from Guatemala have been apprehended by the Border Patrol between October and April. Many have been held in Mexico, which has faced pressure from the US government to restrict migration.
In early December, seven-year-old Jakelin Caal Maquin died of a bacterial infection.
Eight-year-old Felipe Gomez Alonzo died on Christmas Eve of a flu infection. He had been held with his father for a week before falling ill. CBP acknowledged it transferred Gomez Alonzo and his father between stations because it did not have space at the El Paso station. The last place the son and father were hald was a highway checkpoint.
After Gomez Alonzo's death, the Department of Homeland Security announced it would expand medical checks and ensure that all children in Border Patrol custody would receive "a more thorough hands-on assessment at the earliest possible time".
Juan de Leon Gutierrez, 16, died in late April after officials noticed he was sick at a youth detention facility operated by US Department of Health and Human Services. The medical examiner in Corpus Christi, Texas, said Juan had been diagnosed with a rare condition known as Pott's puffy tumour, which can be caused by a severe sinus infection or head trauma.
Gutierrez's mother told Al-Jazeera earlier this month, that the teen left Guatemala in search of opportunities to send money back home after the family suffered from several years of drought in the country's dry cone.
Trump's administration has for months warned that the US immigration system was at a "breaking point". The administration has asked for $4.5bln in emergency humanitarian funding and for Congress to change laws that would allow agencies to detain families longer and deport them more quickly.
Many immigration detention facilities are overflowing and unequipped to house families with young children, especially as the numbers of families crossing the US-Mexico border surge to record highs. The Border Patrol made 99,000 apprehensions on the Southern border just in April. More than half were parents and children travelling together.
In recent weeks, the Border Patrol in El Paso, Texas has held families for hours outside in a car park and under an international bridge. Migrant parents complained of having to sleep at that location on the ground outside or in poor conditions in tents.
The agency this month opened a larger, 500-person tent in El Paso as well as in the Rio Grande Valley in South Texas.