A gunman who killed at least three people and wounded five on a US university campus shot himself dead Monday after a massive police manhunt.

Thousands of students at Michigan State University were ordered to shelter in place after shots were fired in a campus building in the early evening, leaving two dead.

The gunman fled to the students' union, where he killed one more person, sparking a major police operation as officers swarmed the 5,000-acre campus.

Gun violence is alarmingly common in the United States, a country where there are more guns than people and where attempts to clamp down on their spread are always met with stiff resistance.

Police confirmed just after midnight the suspected MSU gunman had shot himself dead a short distance from the university.

"We are sad to report that there have been three confirmed fatalities," Deputy Chief Chris Rozman of the university's police force told reporters.

"This is in addition to the five victims who were injured and transported to the hospital. Some of those five victims still have life-threatening injuries."

Rozman said hundreds of officers from several agencies had been involved in the operation to try to find the gunman, releasing a photograph of a Black man in a baggy blue jacket, and wearing red shoes.

"The suspect in this incident was located outside of the MSU campus," he said.

The "suspect has died from a self-inflicted gunshot wound".

"This truly has been a nightmare that we are living tonight. We are relieved to no longer have an active threat on campus," Rozman said.

Police later said the man had no connection to the university and no motive for the shooting was immediately apparent.

"We have no idea why he came to the campus to do this tonight," Rozman said.

Police refused to give details of the victims, including whether they were students or faculty members of the university, one of the top institutions in the United States.

MSU officials said all campus activities would be canceled for the next 48 hours.

Around 50,000 students are enrolled at MSU, the bulk of them undergraduates, according to the university's website.

Tens of thousands of people die every year in the United States after being shot, and many more are wounded.

Eleven people were shot dead last month when an elderly man opened fire in a dance hall in California, where locals were celebrating Lunar New Year.

Days later a farm worker killed seven colleagues a few hundred miles away.