Camron Harris of Henrico, Virginia, is not a student on campus, nor were four of the people injured, Chesterfield County Police said in a statement.
The victims ranged in age from 17 to 23. One of the injured, a 20-year-old, is a student and has now been released from the hospital, authorities said.
The victims' names have not been released.
Authorities have given no information about a possible motive.
Police obtained eight felony warrants for Henrico, including for malicious wounding and the use of a firearm in the commission of a felony.
It wasn't immediately clear if he had a lawyer who could speak on his behalf.
The university said in an earlier statement authorities were searching for multiple suspects, but police provided no additional information on Saturday evening about the search.
University officials said earlier in the day law enforcement did not believe there was an immediate threat to the campus community, and a campus lockdown had been lifted.
The shooting, just after 1.30am on Saturday, prompted a campus lockdown and came as students were getting ready for the new school year.
It happened near the university's Quad Annexes, where campus police and Chesterfield County officers discovered five people suffering from gunshot wounds outside campus dormitories.
According to the university's website, residence halls opened for students a week ago, and classes resume on Monday.
Many students had just completed the university's "New Trojans Experience" for incoming students.
"We recognise the concern this incident has caused among our students, parents, alumni, friends, and the broader VSU community," the university statement said.
"The safety and well-being of our students remain our highest priority."
Virginia State University is a historically Black university located in Ettrick, Virginia, about 39km south of the state capital of Richmond.
The public university has about 5700 students and was the first fully state-supported four-year college for Black Americans.
Most of its students are undergraduates.
The university has grown in recent years while attempting to improve safety and retain its historic charm, said Arthur Fridrich, the university's former director of distance education, who lives near the campus and visits regularly.
A shooting like this as students returned for classes was heartbreaking for the community, he said.
"To start a new year with this event is very tragic," he said.
"It casts a shadow in the minds of all students, and for some it will be difficult to rid their minds of this term."
