Rights groups say at least five people were detained and 25 homes and offices searched in the third successive day of raids.
Babaryka was considered one of the strongest opponents to authoritarian leader Lukashenko, who has been in power for close to three decades.
The economic sanctions are the most sweeping measures imposed against Belarus so far by the EU and come after President Alexander Lukashenko sparked outrage by intercepting a Ryanair airplane in May to arrest dissident journalist Roman Protasevich.
UK, Canada, EU and US ratchet up pressure on President Alexander Lukashenko by imposing sanctions on several senior officials in Belarus over the forced diversion of a Ryanair plane to Minsk.
New laws aim to silence critics of Belarus President Alexander Lukashenko, whose victory in the presidential vote last year sparked huge demonstrations.
State TV broadcast an interview of journalist Roman Protasevich in which he said he called for anti-Lukashenko protests last year, a confession the opposition, UK and Germany say was "clearly under duress".
Meanwhile, Air France cancelled more flights to Moscow after Russian authorities failed to approve flight plans that avoid Belarus airspace.
White House is calling for "a credible international investigation into the events of May 23" when a Ryanair passenger jet flying from Greece to Lithuania was forced to land in Minsk to arrest opposition journalist Roman Protasevich.
President Alexander Lukashenko dismisses international outcry over incident in his first public statement since diverting a Ryanair flight to arrest dissident journalist Roman Protasevich.
Demonstrations gripped the country for months after authoritarian President Alexander Lukashenko, 66, claimed a landslide sixth presidential term in a vote the opposition and European leaders said was rigged.
A Ryanair passenger flight from Athens to Vilnius was diverted while in Belarusian airspace on Sunday over a supposed bomb threat, prompting a global outcry to Minsk's forced landing of the aircraft to arrest a dissident journalist.
Belarusian authorities scrambled a fighter jet and flagged what turned out to be a false bomb alert to force a Ryanair aircraft to land on Sunday to detain opposition journalist Roman Protasevich, who was onboard.
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