PRAGUE—Czechs on Sunday held their largest protest since the fall of Communism, as hundreds of thousands gathered on a hilltop overlooking the capital to try to prevent the country from joining what organizers see as the increasingly autocratic direction of the region.

The protesters, estimated at 200,000 by police, gathered under Czech flags and atop picnic blankets to rail against Prime Minister Andrej Babis, a billionaire businessman who rode a populist message into power in 2017. The crowd covered the grassy hill that...