A fourth student, a 17-year-old boy, died on Wednesday from wounds he suffered when a sophomore opened fire at a Michigan high school a day earlier, authorities said.

The other victims included a 16-year-old boy who died in a deputy's patrol car on the way to a hospital. Seven people were wounded, some critically, including a 14-year-old girl who was placed on a ventilator after surgery.

Investigators were still trying to determine a motive for the shooting on Tuesday at Oxford High School, located in a community of about 22,000 people roughly 48 kilometres north of Detroit.

Authorities said they were searching the suspect's cellphone, school video footage and social media posts.

"The person that's got the most insight and the motive is not talking," Oakland County Sheriff Michael Bouchard said late on Tuesday at a news conference.

"Deputies rushed to the school around lunch time and arrested the suspect in a hallway within minutes. He put his hands in the air as deputies approached," Bouchard said.

The boy's father on Friday bought the 9mm Sig Sauer used in the shooting, Bouchard said. He did not know why the man bought the semiautomatic handgun, which his son had been posting pictures of and practicing shooting, Bouchard said.

Authorities did not immediately release the boy's name.

The four students who were killed were identified as 16-year-old Tate Myre, 14-year-old Hana St. Juliana, 17-year-old Madisyn Baldwin and Justin Shilling, who died on Wednesday.

Bouchard said Myre died in a patrol car as a deputy tried to get him to an emergency room.

A teacher who received a graze wound to the shoulder left the hospital, but seven students ranging in age from 14 to 17 remained hospitalised through the night with gunshot wounds, he said.

"The gun the boy was carrying had seven more rounds of ammo in it when he surrendered," Bouchard said.

Undersheriff Mike McCabe said the student's parents advised their son not to talk to investigators. "Police must seek permission from a juvenile's parents or guardian to speak with them," he added.

Oakland County Prosecutor Karen McDonald said in a statement that her office expects to issue charges quickly and that an update would be given on Wednesday.

After the attack, authorities learned of social media posts about threats of a shooting at the roughly 1,700-student school.

The sheriff stressed how crucial it is for such tips to be sent to authorities, while also cautioning against spreading social media rumors before a full investigation.

McCabe downplayed the significance of a situation in early November when a deer's head was thrown off the school roof, which he said was absolutely unrelated to the shooting.

The incident prompted school administrators to post two letters to parents on the school's website, saying they were responding to rumours of a threat against the school but had found none.

Bouchard said the student in custody in the shooting had no previous run-ins with his department, and he was not aware of any disciplinary history at school.

“That's part of our investigation to determine what happened prior to this event and if some signs were missed, how were they missed and why," he said.

The district said in a statement that all schools would be closed for the rest of the week.

Isabel Flores, a 15-year-old ninth grader, told Detroit television station WJBK that she and other students heard gunshots and saw another student bleeding from the face. They then ran from the area through the rear of the school, she said.

A concerned parent, Robin Redding, said her son, 12th-grader Treshan Bryant, stayed home on Tuesday after hearing threats of a possible shooting. "This couldn't be just random," she said.

Bryant said he had heard vague threats for a long time now about plans for a shooting.

At a vigil on Tuesday night at LakePoint Community Church, Leeann Dersa choked back tears as she hugged friends and neighbors. Dersa has lived nearly all of her 73 years in Oxford. Her grandchildren attended the high school.

"Scared us all something terrible. It's awful," Dersa said of the shooting.

Pastor Jesse Holt said news of the shooting flooded in to him and his wife, including texts from some of the 20 to 25 students who are among the 400-member congregation.

"Some were very scared, hiding under their desks and texting us, 'We're safe, we're OK. We heard gunshots, but we're OK'. They were trying to calm us, at least that's how it felt," he said.