A woman also was injured when she apparently jumped from the second story of the burning building.
Virginia State Police Sgt. Michael Conroy said police were searching in Wythe and Pulaski counties for Douglas Albert Jaccard, 58, of the Draper area of Wythe County.
A Wythe County Chief Deputy told CBS affiliate WDBJ that some of Jaccard's belongings have been found, and that they think he is still in the area, but wouldn't elaborate.
Police say the incident began around 7:30 a.m. WDBJ reports that authorities suspect Jaccard set his neighbors' house on fire. A woman and teen were inside at the time; both escaped.
Police responded to the shooting scene shortly after, Conroy said. When a Pulaski County deputy arrived, the suspect shot him and fled into a wooded area. He said the deputy was protected by a bulletproof vest.
Pulaski Community Hospital spokeswoman Nancy May said a woman was brought to the hospital about 10:45 a.m. with injuries from jumping out of a burning house.
The deputy was listed in stable condition at the hospital, and May said another shooting victim was transferred to a Roanoke hospital.
Shots were fired at two Wythe County sheriff's deputies but they were not injured, according to Chief Deputy Keith Dunagan of the Wythe County Sheriff's Office.
Tactical teams, K-9 units and a helicopter are being employed in the search, reports WDBJ correspondent Holly Pietrzak.
Sally Hicks, who is related to two of the shooting victims, called WDBJ, saying Jaccard had posed a long-running problem for her family.
"This could have been avoided, if Wythe County law enforcement had heeded to what we have been telling them for months now," Hicks said. "We have been begging them for warrants and everything else. He has been threatening us for months, saying he was going to take care of us and our children, and every time we would call to try to get something done, they would say there was nothing they could do about it."
Jaccard was recently at the New River Valley Jail. He was out on bond and was due in Wythe County Circuit Court Wednesday to enter a plea agreement on two counts of taking indecent liberties with a minor, abduction and possession of explosives by a convicted felon.
Pietrzak reports that the charges on which Jaccard was out on bond involved those same neighbors.
Houses in the area were evacuated. Five schools in Wythe County were locked down, but school officials said all students were safe.
Jaccard is 5'8", 170 pounds, with brown hair and brown eyes. He is believed armed with a high-powered rifle.