The gunman began shooting around 5 p.m. Sunday at a mobile home outside of the town of Louisa, said Louisa County sheriff's Maj. Donnie Lowe.
The man had unleashed a pit bull on officers before he and his dog were then killed in a shootout, Lowe said. No officers were injured, he said.
Police said they had responded to a minor incident at the home earlier in the day.
"It appears that this is all a family-related matter," said Sgt. Thomas Molnar, a state police spokesman.
Molnar said the victims' identities weren't immediately released.
The wounded, including one with life-threatening injuries, were transported to the University of Virginia Medical Center in Charlottesville, Lowe said. A hospital spokeswoman didn't immediately return a telephone message early Monday.
Information from: Richmond Times-Dispatch, http://www.timesdispatch.com