"We will honour you as the most important whistleblower of ourtimes," said Hege Newth Nouri, head of the board of the Bjornson Academy.
The Bjornson Prize award is worth 100,000 kroner (12,000 dollars).
Nouri said she hoped Snowden would be able to receive his diploma and statue next year - in Norway.
She said an empty chair on the stage in Molde, western Norway symbolised that the organisers had failed to secure guarantees Snowden would not be arrested and possibly be extradited to the United States.
In its citation, the jury said Snowden had "shown how the electronic integrated information world can be a threat to personal integrity, and also might pose a threat against freedom of expression."
Snowden, who currently has asylum in Russia, is wanted by the US government on espionage charges for exposing extensive telephone and internet data-collection programmes used by the US National Security Agency (NSA).
In an interview conducted via videolink from Russia, Snowden said he loved the United States and his actions were not anti-American.
"I knew the consequences of my actions when I took them," he said.
"I honestly never expected to be free today, I expected to be inprison, I didn't expect to get awards, I expected my reputation to be ruined because a number of incredibly powerful officials around the world were personally embarrassed because of these revelations," headded.
He said Russia was not his planned destination, but that he had no other option after his passport was cancelled and he did not receive replies from 21 countries where he applied for asylum.
The prize was named after Bjornstjerne Bjornson, a Norwegian author and 1903 Nobel literature laureate.