The magazine said investigators had found the bomb during a search of the girl's mother's apartment.
“It was filled with explosive materials and completely functional,” Bonn public prosecutors told Focus, saying the girl had probably got the bomb-making instructions on the internet.
The girl, who police identified as Tanja Otto, was found late Monday night after spending several hours on the run. She remains in police custody and will face public prosecutors in Bonn on Tuesday, a police spokesperson said. Authorities did not reveal whether the troubled student had been captured by police or if she turned herself in, saying they had continued their investigation throughout the night.
A spokesman for the Bonn public prosecutor said the girl was considered to be at risk of committing suicide and authorities were debating moving her to a youth psychiatric clinic.
On Tuesday, school director Anne Marie Wähner described Otto as “actually a really good student.” But two of Otto's classmates last week told school authorities that the 16-year-old was plagued by problems. They said Otto had often spoken about suicide with her friends.
Another 17-year-old female student was able to stop the arson attack when she happened upon Otto in the girls' bathroom at Albert Einstein high school in Sankt Augustin, some 10 kilometres from Bonn, around 9 am on Monday. Otto then slashed the other girl with a knife and severed her thumb.
The alleged attacker reportedly had several knives, a tear gas pistol, 10 Molotov cocktails, a flame thrower and five kilogrammes of gunpowder, local media reported, adding that her rucksack also contained a suicide letter to police.
Screams alerted teachers to the incident and they called the police to tell them the school was under attack. The injured girl was transported to a Bonn hospital for emergency surgery.
Authorities evacuated some 800 students from the school to a neighbouring athletics building.
Just last week, Otto reportedly threatened to attack the school, for which she was scheduled to meet with a school psychologist on Monday.
Barbara Sommer, North-Rhine Westphalia's minister for schools, said she was concerned that the suspect was a girl, saying girls had “simply not been part of this problem so far.”
Germany is particularly sensitive to school violence after 17-year-old Tim Kretschmer killed 15 people at his former school with his father's gun in the southwestern German town of Winnenden in March. He later killed himself during a shootout with police.
The massacre stirred up debate about stronger whether the country needs stronger gun laws or a ban on violent video games.