Up to 15 other people were reportedly wounded in the incident, which occurred Monday afternoon, FBI spokesman Paul McCabe told a news conference in Minneapolis.
The dead include a female teacher, a male security officer and four students -- two male and two female. They were found in one room.
One of the four dead students is believed to be the teenaged shooter. He was believed to be acting alone. Despite that, the school was cleared of students and staff for security reasons.
In addition, two more people were found dead at a residence.
Red Lake Net News, a website operated by the tribe offering information about the community, said the two dead at the residence were the suspected shooter's grandfather and grandmother.
The grandfather was a veteran law enforcement officer in the community, it said. Other reports say the grandfather was a former law enforcement officer.
"This is a fluid situation," McCabe said, adding more facts will be released as they become available.
Red Lake is located in the far northern part of the state, about 380 kilometres north of the Minneapolis-St. Paul region. It is an Indian reservation for a band of Chippewa Indians.
The high school has about 300 students.
Audrey Thayer, who lives in nearby Bemidji, told The Associated Press the police had locked the reservation down with roadblocks.
With files from The Associated Press