The 43-year-old Salvadoran, who crossed into the US with his daughter, was taken to hospital but later was pronounced dead there, CBP announced on Saturday.
The man was "rushed to the hospital after falling into medical distress," according to the announcement, which added the cause of his death was unknown.
He had been held at the Rio Grande Valley central processing center in McAllen, Texas, for a week, a law enforcement official told the AP.
The man's daughter was still in Border Patrol custody, although officials have requested her transfer to a shelter for children who come to the United States on their won.
The girl, whose age is unknown, will remain there until she is released to a sponsor, a process that could take weeks.
Since December, two other migrant adults and five children have died while being held in government custody.
Last week, more than 300 migrant children were discovered in the overcrowded station, where they have to stay for weeks in filthy conditions without adequate food and water.
The discovery led acting commissioner of CBP, John Sanders, to announce his resignation.
In recent months, advocates have been warning that the number of people dying while crossing the border would increase because they are forced to cross areas which are far more dangerous now that US President Donald Trump has taken strict measures to stem their flow.
Those, who succeed in reaching the US, are kept in detention centers which according to rights groups lack proper conditions.
Trump's immigration policies have sparked protests both inside the US and abroad since he took office in January.