Agents searched Lula's house in Sao Paulo, the offices of the Lula Institute, and houses of family members and associates, said Jose Chrispiniano, a spokesman for Lula and his institute.
As agents, backed by armed officers in camouflage, went through Lula's house, supporters and opponents demonstrated in the street, shouting and scuffling, AFP journalists said.
Prosecutors said Lula was targeted as part of the Operation Car Wash investigation into an embezzlement and bribery conspiracy centered on Petrobras. The corruption scandal, which has already seen a Who's Who of Brazilian politicians and businessmen face charges, is believed to be the biggest ever in Brazil.
Lula was not arrested, but was held for questioning over alleged "favors" received from corrupt construction companies implicated in the Petrobras kickbacks scheme, prosecutors said. The police interview, held at an airport near his home, lasted more than three hours, Globo news site reported.
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Lula, who was president from 2003-2010, remains one of Brazil's most influential figures and his fate is closely linked to that of his successor, President Dilma Rousseff, and the future of the ruling Workers' Party.
Chrispiniano called the search, in which agents were backed by armed officers, "arbitrary, illegal and unjustified."
"The violence carried out today against the ex-president Lula and his family... Is an assault against the rule of law that impacts all of Brazilian society," he said.
The allegations against Lula center on a luxury seaside apartment and country house that authorities say appear to have been given to the ex-president as bribes.
Lula denies ownership of the apartment and any involvement in the Petrobras scheme.