The suspect, who was 13 years old at the time, denied making the online threats and officials “alerted local schools for continued monitoring of the subject”.
“At the time, there was no probable cause for an arrest or to take any additional law enforcement action on the local, state, or federal levels,” added the FBI statement.
Sheriff Jud Smith described the attack as “pure evil” and said officers were on the scene within minutes of receiving 911 calls at 10:20 local time (14:20 GMT).
Two officers assigned to the school “immediately encountered the subject”, the sheriff said, adding that the boy “immediately surrendered”.
The boy has been interviewed and spoke with investigators once while in custody, Sheriff Smith said.
The sheriff added that no motive had been identified and that law enforcement did not know of “any targets at this point”.
Students described chaotic scenes as alerts went out that an attacker was on campus. Classes at Apalachee began last month, but many students across the US are returning to school this week.
Lyela Sayarath, who was in the alleged attacker’s class, told CNN that the suspect left the room at the beginning of an algebra lesson.
She said he came back and knocked on the door, which had locked automatically, but another student refused to let him in after noticing he had a gun.
Lyela told CNN the attacker then went to the classroom next door, where he began shooting.
Marques Coleman, 14, said he saw the attacker holding a “big gun” just before the shooting began.
“I got up, I started running, he started shooting like, like 10 times. He shot at least 10 times,” he told CBS News, the BBC’s US partner.
“My teacher started barricading the door with desks,” he said.
After standing up, the pupil said he saw “one of my classmates on the ground bleeding so bad”, another girl shot in the leg and a friend shot in the stomach.
A vigil was held on Wednesday evening in the city of 18,000 residents about 50 miles (80km) from Atlanta.
This was the 23rd US school shooting of 2024, according to a database maintained by the magazine Education Week, which counts 11 dead and 38 injured in such attacks so far this year.
David Riedman, who runs the K-12 School Shooting Database, told Reuters news agency that the shooting in Georgia was the first “planned attack” at a school during this autumn term.