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The San Antonio Fire Department said 16 other people found inside the trailer were transported to the hospital for heat stroke and exhaustion, including four minors. Officials also said three people were in custody following the incident.
The truck was found next to railroad tracks in a remote area on the city's southern outskirts.
Mexico's Foreign Minister Marcelo Ebrard called the suffocation of the migrants in the truck the "tragedy in Texas" on Twitter and said the local consulate was en route to the scene, though the nationalities of the victims had not been confirmed.
There have been a record number of migrant crossings at the US-Mexico border in recent months, which has sparked criticisms of the immigration policies of US President Joe Biden, a Democrat.
Temperatures in San Antonio, about 250km from the Mexican border, swelled to a high of 39.4degC on Monday with high humidity.
In July 2017, ten migrants died after being transported in a tractor-trailer that was discovered by San Antonio police in a Wal-Mart car park.
The driver, James Matthew Bradley, Jr, was sentenced the following year to life in prison for his role in the smuggling operation.