"It's final: he won't come to Norway on September 5 to receive the prize," Hege Newth Nouri of the Norwegian Academy of Literature and Freedom of Expression, which awards the Bjornson Prize, told AFP.
"Norwegian authorities could not guarantee that he could come without the risk of being extradited to the United States," she said.
The 32-year-old former intelligence contractor fled the US after leaking documents on vast US surveillance programs to journalists, and has been granted asylum in Russia.
Newth Nouri said prize organisers had not ruled out the possibility of giving him the prize one day at the Norwegian-Russian border in the far north.
On Thursday, Norwegian public broadcaster NRK revealed documents that showed the US had in 2013 asked Norway to arrest and extradite Snowden if he came to the Scandinavian country.
The Norwegian government said it had not responded to the diplomatic missives. Local immigration authorities had around the same time rejected an asylum request Snowden submitted to Norway, one of several countries where he sought refuge.
As in 2014, Snowden has been nominated -- along with 272 others -- for the 2015 Nobel Peace Prize, which is also awarded in Norway.
This year's announcement is due on October 9.
The US administration has branded Snowden a hacker and a traitor who endangered lives by revealing the extent of the National Security Agency spying program.
But his revelation that the NSA siphons vast quantities of telephone data from private US citizens struck a cord and Congress has begun to amend once secret laws.