In a tweet, the parliament's right-of-centre EPP group announced the prize and called on Russian President Vladimir Putin "to free Alexei Navalny. Europe calls for his -- and all other political prisoners' -- freedom".
Navalny, also nominated but passed over for this year's Nobel Peace Prize, was jailed in February after returning to Russia from Germany where he was treated for the attack.
The movement headed by the 45-year-old has been banned as "extremist" and some of his allies have been forced to leave Russia under pressure from authorities.
The Sakharov Prize, set up in 1988 and named after Soviet dissident Andrei Sakharov, is awarded every year to those fighting for human rights or democracy.
Last year's award of the 50,000-euro ($58,000) prize went to the movement opposing President Alexander Lukashenko in Belarus, a close ally of Russian President Vladimir Putin.
The prize will be handed out in a ceremony in a plenary session of the European Parliament in December in Strasbourg.
The other finalists for the prize were a group of Afghan women for their fight for women's rights in Taliban-run Afghanistan, and Jeanine Anez, a former head of state in Bolivia who is jailed on charges of leading a coup in 2019.