The victims were all students at the university, police said, and the injured remain in critical condition.

The police said a caller's tip led them to the suspected gunman, who died from a self-inflicted gunshot wound.

The suspect, who has since been identified, had no ties to MSU.

"We can confirm that the 43-year-old suspect had no affiliation to the university. He was not a student, faculty, or staff, current or previous," Chris Rozman of the Michigan State University Police said.

Questions still remain about the motive of the gunman, who was identified as 43-year-old Anthony McRae.

"We have absolutely no idea what the motive was at this point," Mr Rozman said.

The names of the victims have not yet been released. 

Dr Denny Martin, the Chief Medical Officer of Sparrow Hospital, where the victims were taken for treatment, said four of the injured required surgery and one was taken to critical care. All five remain in hospital. 

"This is something that we practice for very often, but never want to do," said a visibly emotional Dr Martin at Tuesday's news conference.

The gunman opened fire shortly before 20:30 local time (01:30 GMT) at Berkey Hall, a building located north of the MSU campus in the city of East Lansing.

Responding officers found multiple students who were injured - two of whom died on the scene. 

Police said the suspect then walked over to the nearby MSU Union building, where they received several more reports of gunshots. The third victim died inside the building, they said. 

The suspect then quickly fled the scene, sparking a large manhunt involving hundreds of officers.

He was found nearly four hours later at 11:45 local time in the City of Lansing, around three miles (4.82 km) northwest of campus, after police released a photo of him and a citizen called in a tip that helped locate him.

The photo, taken from surveillance footage, showed the suspect wearing a denim jacket, a navy baseball cap and red trainers.