Virginia State Police spokeswoman Corinne Geller said more than 100 officers had surrounded the man in a wooded area just outside the town of Appomattox.
She said there had been "multiple deaths" but would not say just how many had been killed.
Police said the drama started just after noon local time when an injured man was found on a rural stretch of road. When officers responded, someone fired at them, and a police helicopter had to land with a ruptured fuel tank. The officers were not injured.
It is not known what prompted the shootings.
Police were trying to determine if the suspect was related to, or worked with, the victims.
Residents near the scene were told to remain inside with their doors locked and a small Christian school was locked down until police could escort about 60 children from the building.
"We're just being cautious, keeping our doors locked, not going outside," said Bethel Hawkins, who lives about two miles up the road from where the shootings occurred. "Our church service is supposed to be tonight, but we talked with our pastor and told him we're not coming out. We're not going out in the dark not knowing what's out there."
Appomattox is best known as the place where Confederate general Robert E Lee surrendered in 1865 to end the US Civil War.