The chase had reached speeds topping 100 miles per hour, the sheriff added.
Border Patrol officials have repeatedly warned of the dangers of smuggling large numbers of people in vehicles.
Sunday's crash came almost a week after more than 50 immigrants were found inside a refrigerated tractor-trailer Monday in San Antonio. Six patients were taken to San Antonio Military Medical Center in San Antonio, Lt. Edwin Roberts said. "This is a ideal example of why our borders need to be secure", he added.
Texas Department of Public Safety officials say four were pronounced dead at the scene midday Sunday.
Boyd said the driver and one passenger of the passengers were the only USA citizens in the vehicle.
Some of the injured were ejected from the Chevy Suburban vehicle.
Authorities are investigating the scene where a vehicle full of undocumented immigrants being chased by Border Patrol agents crashed. That agent stopped one vehicle and radioed a description of the other two vehicles to other agents, the agency said.
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The passenger, also believed to be a US citizen, is now in custody.
He said the driver, whose name was not immediately released, was known to police as a human smuggler. They are likely to face state and federal charges, Boyd said.
Images from the scene appeared to show a large four-door SUV-style auto badly wrecked in the middle of the road.
Border patrol agents use all-terrain vehicles (ATV) to search for illegal immigrants along the US.
It was unclear why law enforcement began chasing the vehicle, though KABB quoted Dimmit County Sheriff Marion Boyd saying it was the result of "good police work".