The male driver was in custody, Lieutenant Martin Sandoval of the Brownsville Police Department said, adding he was charged with reckless driving and could face additional charges.
The incident happened in the city of Brownsville near the Mexican border at about 8.30am local time on Sunday.
Sandoval said the victims in the morning crash were waiting at a bus stop near Ozanam Center, a shelter for the homeless used by migrants. He said some migrants were among the dead.
