Authorities placed two Brownsville schools under lockdown following reports of gunfire on the city's northeast side.
Cameron County Sheriff Omar Lucio confirmed that deputies received a report of a shooting off FM 802 around 10:40 a.m. Monday.
Sheriff Lucio said 35-year-old Roman Garcia was shot in the head following an argument with another man.
Deputies set up a crime scene is located at the El Jardin Superette convenience store.
Authorities searching neighborhoods near the scene of the shooting in search of the suspects and took a man and woman into custody at a home near Corta Street.
Brownsville police blocked off Tallowood Circle in search of those suspects.
Brownsville ISD officials confirmed that both Rivera High School and Vermillion Elementary School temporarily placed under lockdown.
The alleged shooting took place off campus but school district officials placed the schools under lockdown as a precaution.
The lockdowns were lifted just after 11:40 a.m. Monday.
At this time, investigators believe that there are one or two suspects still on the run - one is described as tall and with redish hair.
Sheriff Lucio said Garcia was last listed in critical condition and will be transported to a hospital in San Antonio.