SAO PAULO—A Brazilian federal prosecutor on Wednesday asked a judge to shut down all Chevron Corp. and Transocean Ltd. operations in Brazil in a lawsuit that seeks some 20 billion Brazilian reais ($11 billion) in damages from the companies, the latest legal broadside to the firms since oil leaked from a well they operate in early November.

In a statement announcing the lawsuit, the prosecutor's office in Campos, a city in Rio de Janeiro state, said Chevron and Transocean "showed a lack of planning and environmental management,"...