Police said the suspect, a long-term and current Virginia Beach city employee, fired "indiscriminately" in a public utilities building.
The gunman, whose identity was not released, was killed in an exchange of gunfire with police.
Officials said an officer was wounded when a bullet struck his vest.
How did the shooting unfold?
The attack began shortly after 16:00 (20:00 GMT), at Virginia Beach Municipal Center, in an area which is home to a number of city government buildings. The area was put into lockdown by police and employees were evacuated.
"We just heard people yelling and screaming at people to get down," Megan Banton, an administrative assistant in the building, told local television news station WAVY.
One of the victims was shot outside in a car, and the rest were found over three floors of the government building, Police Chief James Cervera said.
Four officers entered the building and located the gunman inside and "immediately engaged" him, Chief Cervera said. The attacker was then killed in an extended exchange of gunfire.
The police chief said the crime scene was "horrific" and could "best be described as a war zone".
Image copyright Reuters
Image caption The shooting was at Building 2 in Virginia Beach Municipal Center
"I want you to know that during this gun battle, basically the officers stopped this individual from committing more carnage in that building," Chief Cervera said.
Police recovered a rifle and a handgun, thought to have been used by the suspect, at the scene.
What is known about the victims?
The identities of the 12 victims and the suspect have not yet been released. Chief Cervera said the suspect's name would only be released after the victims' families had been notified.
"We're going to mention his name once and then he will forever be referred to as 'the suspect', because our focus now is the dignity and respect to the victims in this case and to their families," he said.
At least four people are known to have been wounded, including a police officer, but the severity of their injuries remained unclear.
The injured officer's life was saved by his bulletproof vest, Chief Cervera told reporters.
A White House spokesman said President Trump had been briefed about the shooting.
The FBI was at the scene helping local authorities investigate the shooting, US media reported.
'The most devastating day'
Virginia Senator Tim Kaine said on Twitter he was "devastated to learn of the tragic shooting tonight in Virginia Beach".
"My heart is with everyone who lost a loved one, and I'm praying for a swift recovery for all those who have been injured," he said.
Source:BBC
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