The parliament gave him several standing ovations as he accepted by video-link from Moscow.
Parliamentarians from "almost all" of the parties attended the ceremony, along with Snowden's father, who travelled from the USA for the event.
His supporters hope that a west European country such as Sweden might grant him asylum. Members of the Green party called for him to be given sanctuary in Sweden.
Philanthropist Jakob von Uexküll, who established the award in 1980, told the parliament: "So Mr Snowden, your Right Livelihood Award is waiting for you. We trust that Sweden will make it possible for you to collect your award here in Stockholm in person in the very near future."
The awards jury, in its citation, said Snowden was being honoured "for his courage and skill in revealing the unprecedented extent of state surveillance violating basic democratic processes and constitutional rights"
Edward Snowden wins Swedish human rights award for NSA revelations [Ewen MacAskill/The Guardian]