Governor Greg Abbott identified the gunman as 18-year-old Salvador Ramos, who lived in the city and entered the school with a handgun and possibly a rifle.
Fourteen children and one teacher have been killed in a shooting at a primary school in Texas, the state governor has said.
The attack happened at Robb Elementary School in the city of Uvalde, around 80 miles west of San Antonio, Sky News reports.
Governor Greg Abbott identified the gunman as 18-year-old Salvador Ramos, who lived in the city and entered the school with a handgun and possibly a rifle.
Mr Abbott added that the gunman is dead and is believed to have been killed by responding officers.
"He shot and killed horrifically, incomprehensibly, 14 students and killed a teacher", he told a news briefing.
More than a dozen children were taken to Uvalde Memorial Hospital, while University Hospital in San Antonio, said a 66-year-old woman was in critical condition.
White House press secretary Karine Jean-Pierre has said US President Joe Biden has been briefed on the shooting.
Robb Elementary School has an enrollment of just under 600 students.
As an elementary school, classes will be for children aged between around five and 11 years old.
Earlier, The Uvalde Consolidated Independent School District said that all schools in the district were locked down because of gunshots in the area.
A heavy police presence surrounded the school Tuesday afternoon, with officers in heavy vests diverting traffic and FBI agents coming and going from the building.
Uvalde is home to about 16,000 people and Robb Elementary is in a mostly residential neighborhood of modest homes.