Two victims were transported to a hospital, where one died, while a third person believed to also be a victim took themselves to another hospital, according to Old Dominion Chief of Police Garrett Shelton.
All three were affiliated with the university, he said.
Shelton said he would not identify the deceased victim until officers could notify the family.
In a posting on its website, the university said there was no longer a threat but urged the public to avoid the scene of the shooting where emergency personnel continued to work.
Classes and campus operations were cancelled for the rest of the day.
The university's initial alert said that the gunman opened fire at 10.49am in a classroom in Constant Hall, the centre of the university's College of Business.
By midday, police vehicles with flashing lights had blocked off streets around the Norfolk campus.
The university, founded in 1930, serves about 24,000 students, according to its website.
University President Brian Hemphill said in a statement to the school community that Old Dominion had "faced a tragedy" and thanked police and emergency responders for swift intervention.
Virginia governor Abigail Spanberger wrote on Facebook that she had spoken with university leadership and was mobilising state support to assist with the situation.
with AP
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