Natalie Rupnow, who went by Samantha, also injured six others -- leaving two in critical condition, according to officials.
She was dead of an apparent self-inflicted gunshot wound when police arrived on the scene at about 11 a.m. on Monday.
Rupnow had attended the school along with some 390 students in grades Kindergarten through 12, police said.
"I don't know whether [the shooter] was transgender or not," Madison Police Chief Shon Barnes said at a news conference on Monday night, when asked about Rupnow's gender identity.
"I don't think that whatever happened today has anything to do with how she or he or they may have wanted to identify," he said. "And I wish people would kind of leave their own personal biases out of this."
"So, whether or not she was, he was, they were transgender is something that may come out later -- but for what we're doing right now, today, literally eight hours after a mass shooting in a school in Madison, it is of no consequence at this time," Barnes said.
The teen shooter used a handgun, police said. Authorities are investigating the origin of the firearm, according to Barnes.
They are also speaking with her father and "trying to determine what he knew or may have not known about what happened today," Barnes said.
"But again, he lost someone as well," Barnes added.
The family is cooperating, Barnes said, and he explained that police are not currently looking to extend charges in connection with the deadly shooting.
"The parents are fully cooperating, we have no reason to believe that they have committed a crime at this time," Barnes said.
Police activity on the north side in Madison was confirmed as being related to the incident on Monday afternoon. Later in the evening, officials said it was the home of the shooter and that authorities were conducting a search.
The incident took place shortly before 11 a.m. local time on Monday.
"The shooting happened inside a classroom in a study hall of students from mixed grades," Barnes said.
A second-grader called 911 as the attack unfolded.
"Let that soak in for a minute," Barnes said. "A second-grade student called 911 at 10:57 a.m. to report a shooting at school."
Police believe that the suspect was in school when the attack began, and that there wasn't any breach.
However, detectives are investigating whether there were any potential warning signs, Barnes said.
The school does not have metal detectors or a school resource officer, but has other security protocols in place, according to a representative from the school.
There are cameras inside the building, police confirmed.
The school representative also confirmed that the faculty and students had been trained in lockdown procedures, which were implemented during the active shooter incident on Monday.
As of Monday evening, two of the six injured were released from SSM Health St. Mary's Hospital.
Two others are reported in stable condition, while two are in critical condition with life-threatening injuries, officials said.
The identities of the victims have not yet been made public.
This is a developing story. Please check back for updates.