A second man was also shot dead a short while later, Upper Austria police spokesperson Ulrike Handelbauer told CNN on Monday.
A large-scale police operation with helicopters and special forces was under way, she said.
Police said Roland Drexler, 56, is suspected of having killed the two men and made a getaway in a Volkswagen Caddy.
“The man is believed to be extremely dangerous and armed,” police said.
A dispute over hunting rights appeared to have sparked the incident, police added. It was not immediately clear why a long-running feud had escalated.
According to Kronen Zeitung, a local outlet, the suspect was known to hunters in the area. “He was a difficult person,” said a hunter from the area who wished not to be named.
The shooting shocked officials at the People’s Party (OVP) regional headquarters in Linz.
“It’s madness,” said state party leader Florian Hiegelsperger.
Herbert Sieghartsleitner, the state hunting master, said the incident was “unbelievable”.
“I am deeply shocked by what has happened. I knew Franz Hofer very well personally,” he said, according to Kronen Zeitung.