The official cause of death will be released by the Dane County Medical Examiner pending autopsy results.
Mr Barnes said that, to his current knowledge, police had not had any prior interactions with the alleged shooter.
Officers responded to a 911 emergency call of a shooter at the Christian school around 11:00 local time (17:00 GMT) on Monday. The attacker attended school before the shooting, Chief Barnes said.
The shooting was confined to a study hall with students in mixed grades.
Barbara Wiers, director of relations at the school, said the school had conducted active shooter training earlier this year and the information was "very fresh" for educators to put into practice on Monday.
She said while the school does not have a dedicated police officer, known as a school resource officer, the doors of all classrooms automatically lock and anyone wanting to gain entry to the campus must be buzzed in through the primary entrance.
Ms Wiers, who said she was teaching at the time of the attack, said students handled themselves "brilliantly".
"They were clearly scared," she said. "When they heard 'lockdown, lockdown' and nothing else, they knew it was real."
Police say they found the shooter dead when they arrived at the school, along with a handgun. No officers fired weapons.