SÃO PAULO, Brazil—A new figure looms over Brazil’s already volatile politics, stirring controversy wherever it goes: A 50-foot-tall balloon depicting Brazil’s former President Luiz Inácio Lula da Silva in a striped jailhouse uniform, complete with ankle ball-and-chain.

The balloon, recognizable as Brazil’s best-known politician because of its big belly and gray beard, first appeared at a mass demonstration in mid-August. Overnight, it became a national mascot for protesters seeking to oust leftist President Dilma Rousseff,...