The students were injured when a gunman opened fire in the cafeteria at Chardon High School, the FBI said, which was busy at breakfast time.
Two of the injured were taken by helicopter to Hillcrest Hospital in Mayfield Heights, and three others went by ambulance to Cleveland Hospital.
Authorities say one gunman was involved, and he has been arrested.
An official said that four boys and one girl were injured in the shooting.
All schools in Chardon will be closed on Tuesday and a vigil has been scheduled for Tuesday evening.
“We are shocked by this senseless tragedy,” Daniel Parmertor’s family said in a statement.
“Danny was a bright young boy who had a bright future ahead of him.”
Ambulances arrived from Chardon as well as from three nearby towns within 30 minutes of the shooting, which happened at 07:30 local time.
The two students who were airlifted to hospital were listed in critical condition on Monday afternoon, with one additional student in serious condition and one in stable condition.
Local news reports said the gunman was chased out of the building by a teacher before turning himself in to two people in the vicinity of the school.
“I am happy to tell you that the student that did the shooting is captured,” a sheriff’s official said to reporters at the scene.
“He actually turned himself in to a couple of innocent bystanders just north of the city here in Chardon township.”
Some students said they recognized the shooter, but police said the suspect would not be identified because he was a juvenile.
By early Monday afternoon, police and FBI had surrounded a house in a nearby rural neighborhood.
FBI officials would not comment on a motive.
However, Danny Komertz, 15, who witnessed the shooting, said the gunman was known as an outcast who had apparently been bullied.
One boy who was in the cafeteria when gunfire broke out told US news channel MSNBC: “I thought it was firecrackers at first, I wasn’t sure.
“And then I saw a bunch of people running out. So I started running… I heard someone yell behind me: <<Get down>.. And I heard a bunch of shots fired behind me.”
Students were evacuated to a nearby elementary school, where parents flocked to collect them. Chardon High School has about 1,100 pupils.
Officials from a number of law enforcement authorities rushed to the scene, with a special operations team said to have combed the school for evidence.
The Bureau of Alcohol, Tobacco, Firearms and Explosives has sent a team of eight agents to trace the firearm.
Chardon, a town of about 5,000 residents, is located about 30 miles (48km) east of the city of Cleveland.
US high schools and university campuses are no stranger to gun attacks, and many have well-drilled security and emergency response procedures in place aiming to prevent attacks and manage the response if a gunman does attack.
Monday’s shooting was the worst incidence of gun violence at a US high school in 11 months and the worst shooting in Ohio since late 2007, the Brady Center to Prevent Gun Violence told Reuters news agency.
In the most notorious shooting, two students at Columbine High School in Colorado killed 12 students and a teacher in April 1999.
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