No one was injured in the fire early Saturday.
Three men were arrested Tuesday: Jose Luis Hernandez, 19, and his brother James Robert Hernandez, 18, both of Lubbock, and Juan Cruz Dominguez, 19, of Abernathy, said Felix Garcia, resident agent in the Lubbock office of the Bureau of Alcohol, Tobacco and Firearms.
The other suspect, 16, is a sophomore at Abernathy High and was to have a detention hearing Wednesday. Police detained him Monday at his home, and he was being held in the Garza County Juvenile Detention Center.
Other arrests are expected, Garcia said.
The junior high area sustained the worst damage, and parts of the building could be closed for months. About 200 of the school's 805 students were displaced and have been going to class in available space in the administration building and elementary school, officials said.
An Abernathy police officer noticed smoke coming from the school about 5 a.m. Saturday. Investigators suspected foul play immediately because the building had been broken into and graffiti was sprayed inside, Garcia said.
Abernathy is about 20 miles north of Lubbock.