"If we are to live in a liberal society, we must stand and defend liberal values," the former National Security Agency worker said from exile in Russia.
"Government and society are built on trust."
The Stuttgarter Peace Prize was established in 2003 by citizens' group, Die AnStifter. The award comes with a €5,000 cash prize.
In an introductory, Ines Pohl, editor-in-chief of the left-leaning tageszeitung, thanked Snowden for opening "a new perspective on secret service doings that are threatening our freedom and privacy".
She went on to criticize Snowden's homeland for the acts he has been responsible for exposing.
"We have come to realise that in the USA ... a deceitful surveillance state has established itself with the assistance of its secret services, by exploiting its citizens' fears after 9/11 to install mechanisms of control one would rather take for science fiction."
Snowden's acceptance speech was delayed by technical issues and at one point was unclear if it would work to establish a connection through "five corners to Moscow" said Fritz Mielert, the head of Die AnStifter.
Once connected, the 31-year-old said the world needs activists.
"I will do what I can," he said.
Snowden has been living in exile in Russia since 2013 after he met with three journalists in a Hong Kong hotel room to expose the extent of the NSA's reach into the private lives of citizens and governments around the world.
He faces charges of espionage and theft of government property in the US and has had his passport revoked as a result of his acts.
As long as he stays in Russia, he will not be extradited to face charges.
A campaign in Germany has called on the government to ignore the US's extradition request and grant the whistleblower asylum. However, earlier this month, a parliamentary question revealed that Snowden has dropped his appeal for residency.
Snowden's leaks revealed that the NSA had also been spying on Chancellor Angela Merkel and the CIA station chief in Berlin was expelled in July as a result of further revellations.
In an interview with German television in Moscow, the former intelligence operative said that the NSA also partook in industrial espionage against German companies.