Given the interests at stake, it is essential that there be no doubt about what caused the plane to fall.
Teori Zavascki, 68, died Thursday when the light plane in which he was flying went down off the coast of Rio de Janeiro state, killing all five people on board.
Federal police are investigating, a spokesman told AFP.
Zavascki had been working on compiling the confessions of construction executives involved in the huge corruption scandal at state oil firm Petrobras.
"I think it has to be investigated in depth, because isn't it too much of a coincidence?" the judge's son Francisco Prehn Zavascki was quoted as saying by newspaper Valor.
"We hope it was just an accident."
One of the top judges in the case, Sergio Moro, said he was "perplexed" by Zavascki's death.
The incident "demands a rapid and transparent investigation," wrote columnist Bernardo Mello Franco in the Folha de Sao Paulo newspaper.
"Given the interests at stake, it is essential that there be no doubt about what caused the plane to fall."
Veja magazine quoted a sailor on a boat who saw the plane crash as saying it was giving off smoke before it went down.
Media have speculated that the executives' testimony could implicate President Michel Temer in the scandal, which has ensnared much of Brazil's business and political elite.
Temer is now responsible for choosing Zavascki's successor.