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The victims were rushed to area hospitals where a boy identified as Daniel Parmertor, 16, died at MetroHealth System in Cleveland.
Parmertor, a high school junior, went to a nearby vocational school where he studied computer science and was waiting in the cafeteria for a bus when the gunman opened fire.
"We are shocked by this senseless tragedy," said a statement from Parmertor's family, provided by MetroHealth. "Danny was a bright young boy who had a bright future ahead of him. The family is torn by this loss. We ask that you respect our privacy during this difficult time."
Police have not formally identified the gunman, but students, parents of students and local media said his name was T.J. Lane. By early afternoon, police and FBI had surrounded a brown house on Wilder Road in a rural, wooded area of Chardon identified in public records as belonging to Thomas Lane.
Two of the four other victims were in critical condition at MetroHealth, according to Chardon Police Chief Tim McKenna. A 17-year-old boy was in serious condition and an 18-year-old girl was stable at Hillcrest Hospital in suburban Cleveland, a spokeswoman said.
Geauga Sheriff's department officials said the suspect was caught about half an hour after the shooting with the help of citizens and a police dog. The teacher who chased the gunman from the school was not identified.
The shooting took place at around 7:30am (local time) while students were in the cafeteria studying, eating breakfast and waiting for buses. Chardon High School student Danielle Samples, 16, who was in the cafeteria at the time, told Reuters she heard a series of "pops" and someone yelled to run down the hallway into a classroom. While Samples was in the hall, she heard another round of pops.
"It hasn't hit me yet," Samples said of the experience. "It's very surreal."
She said the shooter was at Chardon's cafeteria waiting for a bus. She said the student lived with his grandparents and sister.
The Ohio shooting is the worst at a US high school in 11 months and the worst in Ohio since late 2007, according to the Brady Center to Prevent Gun Violence.
US Secretary of Education Arne Duncan said in a statement that the shootings "are an unspeakable tragedy."
"It's still too early to know yet why a student took a firearm to school and shot his classmates. But preliminary reports indicate that if it were not for the extraordinary courage of a teacher who chased the shooter out of the school, and if not for the speedy reaction of school leaders, the toll of these shootings could have been even worse," Duncan said.
Chardon student Sofia Larkins, 14, was sitting with Lane's sister when the shooting began. "She didn't know anything," said Larkins. "She was surprised as anyone."
The two girls fled to a teacher's lounge when the shooting began and began hearing talk that T.J. was the shooter, Larkins said. His sister began crying.
Larkins said school officials came to the lounge and took his sister away for questioning. Fellow students described T.J. Lane as quiet.
Chardon, the seat of Geauga County, is a semi-rural, fairly well-educated and affluent town about 56km from Cleveland about 5,000 residents. Neatly restored brick buildings dot its downtown with quaint offices and shops, and the city's website says it is the center of the state's maple syrup industry.
After the shooting, emergency vehicles rushed to the high school, where solemn students streamed from the building to meet parents. The entire school district was closed for the day and will be closed Tuesday.
"We want them to stay home and spend some time reflecting on family," said an emotional Joseph Bergant, superintendent of Chardon schools, at a news conference. He praised the actions of teachers, who had been through disaster training and acted quickly to protect the students.
Some of the injured students attended Auburn Career Academy, a vocational school with 700 juniors and seniors taken from 11 surrounding school districts including Chardon.
The deadliest school shooting in the United States was the 2007 massacre at Virginia Tech University that left 33 people dead. The worst high school shooting was the 1999 attack at Columbine High School in Colorado that killed 12 students and a teacher.