The gunman opened fire at Robb Elementary School – which teaches children aged seven to 10 – in the city of Uvalde before he was killed by law enforcement, officials said.
The 18-year-old suspect had a handgun, an AR-15 semi-automatic rifle and high-capacity magazines, investigators say.
The teenager is suspected of shooting his grandmother before the rampage.
Local media report he may have been a high school student in the area.
Uvalde Consolidated Independent School District Chief of Police Pete Arredondo said the shooting began at 11:32 local time on Tuesday, and that investigators believe the attacker “did act alone during this heinous crime”.
Texas Governor Greg Abbott said the shooter, whom he named as Salvador Ramos, abandoned a vehicle before entering the school to “horrifically, incomprehensibly” open fire.
Several of the children who died have been identified.
Family members confirmed the deaths of 10-year-olds Xavier Lopez and Amerie Jo Garza in statements on Tuesday night.
Angel Garza said on Facebook that his daughter Amerie had been killed.
“My little love is now flying high with the angels above. Please don’t take a second for granted. Hug your family. Tell them you love them,” he said.
The two adults who died were both teachers – Irma Garcia and Eva Mireles.
According to the school district’s website, Mrs Garcia is a mother-of-four and had been a teacher for 23 years. The same website says that Ms Mireles had been a teacher for 17 years, has a daughter in college and loved running and hiking.
Nearly 500 pupils are enrolled in the predominantly Hispanic school around 85 miles (135km) west of the city of San Antonio.