The prize, which was launched as an alternative to the Nobel prizes, honours those who work to improve the lives of others.
US whistleblower Edward Snowden has been revealed as this year's winner for his "courage and skill in revealing the unprecedented extent of state surveillance violating basic democratic processes and constitutional rights," the organization said in a statement.
Snowden has been holed up in Russia ever since he leaked top secret NSA documents to journalists last year. He faces up to three decades in prison.
Sveriges Television revealed Snowden's win - which was scheduled to be announced on Thursday - and reported that the foreign ministry was banning the independent organization from making its traditional announcement on at Stockholm's Ministry of Foreign Affairs, even though the award has been handed out there for the past 18 years.
Officially, the ministry has said the ban is based on new security regulations, but SVT reported that it was Sweden's Foreign Minister Carl Bildt who had reacted strongly to the news. Bildt has denied that he was involved in the decision.
The award will be shared by four other laureates, three of whom will share a cash prize of 1.5 million kronor ($210,000).
The civil rights organization said it was in talks with Snowden's lawyers in an effort to get him to Stockholm to accept the award. It will be presented on December 1st in the Swedish Parliament.