Department of Public Safety Trooper Johnny Hernandez says the victims were wearing helmets and using lights on their bikes when the accident happened around 7 p.m. Tuesday.
Hernandez on Wednesday told The Associated Press that it was dark during the wreck in Donna. One bicyclist died at the scene, another died at a hospital and the third remains hospitalized. Their names and hometowns weren't immediately released.
KRGV-TV reports the car hit the oncoming bicyclists while trying to pass another vehicle.
Hernandez says the driver, from Mexico, ran away but later surrendered at the Progreso Port of Entry. Formal charges are pending.