The shooting occurred at about 3pm (21:00 GMT) at Red Lake High School in a rural town in the northern part of the state and on the Red Lake Indian Reservation.
Among the dead at Red Lake High School were a security guard, a teacher, three students and the gunman, with as many as 15 others injured, FBI agent Paul McCabe said.
Some were being cared for in Bemidji, about 30km south of Red Lake. The authorities have closed the reservation while they investigate the shootings.
"They believe the shooter is among the dead and was acting alone," McCabe said.
Prior to Monday afternoon's school shooting, the student shot dead a couple at a home on the reservation, McCabe said.
The couple were the student's grandparents who lived in the village of Red Lake, other officials said. The grandfather was identified on the tribe's website as tribal police officer Daryl "Dash" Lussier.
After shooting his grandparents, the student went to his school and opened fire.
"He came into the school and the first person he shot was the security officer at the door," said Molly Miron, editor of the Bemidji Pioneer newspaper, who talked to students and teachers.
Smiling and waving
"One of the students told me he pointed his gun at a boy and then changed his mind, smiled, waved at him, and shot somebody else," Miron said. Students said he was armed with a rifle or possibly a shotgun.
Red Lake Fire Director Roman Stately said the shooter had two handguns and a shotgun.
"One of the students told me he pointed his gun at a boy and then changed his mind, smiled, waved at him, and shot somebody else"
Molly Miron, editor of Bemidji Pioneer newspaper
Students and a teacher, Diane Schwanz, said the shooter tried to break down a door to get into her classroom.
"I just got on the floor and called the cops," Schwanz told the Pioneer. "I was still just half-believing it."
Ashley Morrison, another student, had taken refuge in Schwanz's classroom. With the shooter banging on the door, she dialled her mother on her mobile phone. Her mother, Wendy Morrison, said she could hear gunshots on the line.
"'Mom, he's trying to get in here and I'm scared'," Ashley told her mother.
All of the dead students were found in one room. One of them was a boy believed to be the shooter, McCabe said.
He would not comment on reports that the boy shot himself and said it was too early to speculate on a motive.
The school was evacuated after the shootings and locked down for investigation, McCabe added.
"It will probably take us throughout the night to really put the whole picture together," McCabe said.
Minnesota governor Tim Pawlenty released a statement offering his condolences to "the families who lost loved ones in this senseless tragedy".
"We ask Minnesotans to help comfort the families and friends of the victims who are suffering unimaginable pain by extending prayers and expressions of support"
"We ask Minnesotans to help comfort the families and friends of the victims who are suffering unimaginable pain by extending prayers and expressions of support," the governor added.
It was the deadliest US school shooting since the April 1999 Columbine High School massacre in Colorado in which 14 students - including the two killers - and a teacher died.
The last apparent fatal school shootings involving a student also happened in Minnesota in September 2003, when two students were killed at Rocori High School in Cold Spring.
Classmate John Jason McLaughlin, who was 15 at the time of the shooting, awaits trial in the case.
The Minnesota reservation is about 400km north of the Twin Cities of St Paul and Minneapolis and 100km south of the Canadian border.
It is home to the Red Lake Ojibwa tribe, commonly known as the Chippewa tribe - one of the poorest in the state.
The Chippewa say they have about 10,000 members, half of whom live on the reservation.
According to a 2000 census, 5162 people lived on the reservation, and all but 91 were full-blooded Indians.
Red Lake High School, on the Red Lake Indian Reservation in far northern Minnesota, has about 300 students, according to its website.