The parliament's president, Josep Borrell of Spain, said this year's prize recognizes the work of journalists "who risk their lives every day in seeking out the truth and passing it on to the citizens of Belarus."
He praised independent Belarusian media for promoting European values in a country that he said remains a "remnant of the past" 15 years after the fall of the Berlin Wall.
The prize was received by a BAZh delegation headed by its president, Zhanna Litvina.
Addressing the parliament, Litvina said the prize was a "very important" recognition not only of the importance of the free media in Belarus, but the right of its citizens to receive objective, noncensored information.
She said President Alexander Lukashenka has cut off Belarus from Europe and its values.
"Unfortunately, Belarusian authorities have succeeded in creating in our country a closed society. This society is built on isolation and ignores democratic values. Sadly, I'm forced to note today that the current regime associates its security and stability with the method of total control over the dissemination of information," Litvina said.
Litvina also urged the EU to continue to put pressure on Lukashenka.
"It is very important to us that European society, European institutions do not give way in their support for the principles of free speech and human rights. This is because as soon as these principles, this position weaken, the repressive apparatus inside the country start working even harder and we will come under even stronger pressure," Litvina said.
The prize was created in 1988 in honor of Soviet dissident Andrei Sakharov, a Russian nuclear physicist. Its recipients have included Burmese pro-democracy leader Aung San Suu Kyi, the Sarajevo daily newspaper "Oslobodjenje," Leyla Zana, a Kurdish activist in Turkey, and Xanano Gusmao, the leader of the East-Timorese independence movement.
The parliament website notes that almost all its winners "have paid dearly for their commitment to defending human dignity, and many have faced persecution, loss of personal freedom or exile."
Borrell described Belarus as a "dictatorial system."
And the parliament's president, a Catalan, used a mixture of Belarusian and Spanish to congratulate Litvina for the work of her organization, which encompasses the efforts of roughly 1,000 people.
Litvina said the Lukashenka government intensified its crackdown on free media after elections in October that were not recognized by the United States or European Union.
She ran through a long list of journalists imprisoned by a government intolerant to all forms of criticism. She and Borrell both mentioned Dmitri Zavadksy, the opposition journalist whose disappearance in the summer of 2000 has never been explained.
Litvina said authorities have increasingly resorted to confiscating entire print runs of newspapers that they claim violate the country's media laws.
She said it's becoming harder to find printing presses and that five major papers are now printed in the Russian town of Smolensk.
Litvina urged the EU to take action against the media crackdown.
"First, we need support for all that still legitimately functions in Belarus. I have in mind above all the independent media, nongovernmental organizations that are active in the country. It is very important to us to strengthen the presence of the European Union in Belarus, in ways such as the [nomination] of a special EU representative for Belarus," Litvina said.
Litvina said Belarus urgently needs a message from the EU that it can still earn a place in Europe. She said Lukashenka may be the face of Belarus today, but at least half of the country's 10 million people link their future to Europe.