The teen-ager, whose identity is not being released because he is a minor, was being held Sunday at a Tarrant County juvenile detention facility, police said.
Police Capt. Bob Willbanks said the youth has not given a statement to authorities.
Investigators believe the fire started near the principal's office before burning through school offices, a chemistry lab and part of the cafeteria. No injuries were reported in the afternoon blaze at 930 Bowman Springs Road.
Sunday morning was the earliest investigators could safely enter the burnt wing of the building because part of the roof was damaged, Willbanks said.
Agents from the Bureau of Alcohol, Tobacco, Firearms and Explosives examined the scene with an accelerant-detecting dog but could not find anything, Willbanks said.
"At this point we don't know what caused it," but there is evidence of arson, Willbanks said.
Police said they are not looking for other suspects.
No damage estimate was available late Sunday, schools Superintendent Gary Dugger said.
"We've called the insurance people to come and look at it, but it's going to have to wait until we can really get in there," Dugger said.
Summer programs were not scheduled at the school, and it's not clear whether the damage is extensive enough to affect operations in the fall.
On Sunday afternoon, the only evidence of fire damage visible from outside was yellow tape blocking off the west side of the building and smoke damage around the edge of the roof.
