Ensaf Haidar told the packed assembly that her husband, sentenced to 1,000 lashes and 10 years in prison for insulting Islam, believed "freedom of expression is like the air that we breathe."
"It would have been nice if my husband could have received the prize personally," Haidar said as his award was placed on an empty chair.
Haidar entered parliament in the eastern French city of Strasbourg to sustained applause, carrying a framed photograph of her husband and calling for a minute's silence to mark the victims of last month's deadly jihadist attacks in Paris.
Parliament head Martin Schulz called on Saudi King Salman "to grant mercy to Raif Badawi and without further ado release him and allow him to return to his family."
Schulz blasted Saudi Arabia's rights record despite it having signed up to the UN Declaration on Human Rights and expressed dismay at this year's more than 150 executions, usually carried out by beheading with a sword.
"This is not a valid way of proceeding in the 21st century," he said, stressing that nothing -- considerations of security cooperation, the country's vast oil wealth -- would stop the EU speaking out when human rights are under threat.
Badawi, 31, was arrested in 2012 and his initial public flogging of 50 lashes in January sparked an international outcry against Saudi Arabia and its human rights record.
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- 'Blasphemy, decadent' free speech -
He co-founded the Saudi Liberal Network Internet discussion group which promoted free speech and sought an end to the influence of religious leaders on public life in one of the world's most conservative countries.
Haidar, who now lives in Canada with the couple's three children, said progress depended on a country allowing freedom of thought, urging Arab rulers to embrace the future instead of clamping down.
"An intellectual in an Arab country has always had to beat about the bush to get his message across. In some, their views are considered blasphemy, decadent," she said, warning of an exodus of free thinkers.
"In the Arab world under the yoke of theocratic regimes they call on citizens to nod and accept everything religious leaders tell them," she said, speaking in Arabic.
Amnesty International welcomed the award as shining a "clear light" on Saudi Arabia's rights record but berated the EU for a "deafening silence" when it comes to seeking his release.
"By cooperating with Saudi Arabia and failing to simultaneously and publicly condemn their human rights' violations, the EU is essentially giving the green light for abuses to continue," it said in a statement.
The Sakharov human rights prize is worth 50,000 euros ($54,000) and awarded every year to honour individuals who combat intolerance, fanaticism and oppression.
Past winners include Pakistani education campaigner Malala Yousafzai, late South African rights icon Nelson Mandela and Myanmar activist Aung San Suu Kyi.