Rondeau played a crucial role in starting work on an ambitious series of infrastructure projects aimed at boosting economic growth and preventing future electricity shortages.
Federal police suspect Rondeau received a 100,000 reais ($51,000) kickback from a construction company that won a government contract to bring electricity to poor households.
Police have already arrested 50 people for siphoning money from infrastructure projects, including Rondeau's senior adviser - in what was dubbed Operation Razor.
The crackdown has raised concerns over Lula's $250bn, four-year plan on public and private investment in roads, railways and airports.
The plan has also included controversial hydroelectric plants in the Amazon region.
Rondeau would be the first minister of Lula's second term, which started in January, to quit over corruption allegations.
Previous scandals including bribery and vote-buying in congress ousted two ministers in Lula's first term, Jose Dirceu, his then chief-of-staff and Antonio Palocci, the finance minister.
Lula has denied involvement in the alleged corruption schemes and insists that federal police are free to investigate any leads they have.
Rondeau commands a large budget, makes policy on Brazil's leading bio-fuels programme, and sits on the board of state-controlled oil company Petrobras.
Federal police said they suspected he may have received a $51,000 kickback from a construction company that won a government contract to bring electricity to poor households.
Tarso Genro, the justice minister, confirmed the investigation but said there was no proof directly implicating Rondeau.
Adriano Pires, head of the Brazilian Centre for Infrastructure consultancy, said the government should move quickly to replace Rondeau if he is forced to quit.
"The electricity sector already has investment problems, delayed projects, infighting over environmental permits. Everyone is worried about possible power shortages," he said.