FBI investigators said the shooter, a classmate, opened fire in the cafeteria at around 7:30 a.m. ET at Chardon High School, about 30 miles east of Cleveland.
A student who saw the attack up close said it appeared that the teenage gunman targeted a group of students sitting together and that the one who was killed was gunned down while trying to duck under the cafeteria table.
The suspect was chased from the building by a teacher and was taken into custody near his car about half a mile away from the high school.
The suspect's name isn't being released because he is a juvenile. FBI officials would not comment on a motive.
The victims were transported to hospitals, where one later died. A Cleveland hospital identified the slain student as Daniel Parmertor, who was shot while waiting for the bus for his daily ride to a vocational center.
"We are shocked by this senseless tragedy," his family said in a statement. "Danny was a bright young boy who had a bright future ahead of him."
Parmertor's teacher at Auburn Career School had no idea why Parmertor, "a very good young man, very quiet," had been targeted, said Auburn's superintendent.
Two of the wounded were listed in critical condition and another was in serious condition.
The FBI is not commenting on a motive. But a student who witnessed the shooting said the gunman was known as an outcast who had apparently been bullied. Others, however, disputed that he had been bullied.
"I looked up and this kid was pointing a gun about 10 feet away from me to a group of four kids sitting at a table," said 15-year-old Danny Komertz. He said the gunman fired two shots quickly, and students scrambled for safety. One of them "was kind of like hiding, trying to get underneath the table, trying to hide, protecting his face."
"Everybody just started running," said 17-year-old Megan Hennessy, who was in class when she heard loud noises. "Everyone was running and screaming down the hallway."
Heather Ziska, 17, said she and several others immediately ran outside after seeing the shooter, while other friends ran into a middle school and others locked themselves in a teachers' lounge.
Schools in the area were locked down and all classes in the district were canceled. About 1,100 students attend Chardon High School.
Grief counselors were on hand at a local middle school. All Chardon schools have been canceled Tuesday. A candlelight service is also being planned for Tuesday evening at a church across from the school.
ABC News and the Associated Press contributed to this story.