SÃO PAULO—A corruption probe threatening to engulf Brazil’s government intensified as police arrested a former top minister of ex-President Luiz Inácio Lula da Silva for allegedly orchestrating a scheme that looted billions of dollars from oil giant Petróleo Brasileiro SA.

Authorities say José Dirceu, who served as Mr. da Silva’s chief of staff from 2003 to 2005, was one of the principle architects of a bid-rigging-and-bribery ring that funneled money stolen from state-run Petrobras into the pockets of politicians and parties,...