The Los Angeles Times reported the investigation involves the appearance of a monetary reward for a supporter of former French President Nicolas Sarkozy.
Lagarde was Sarkozy's finance minister in 2008, when she referred a 20-year old legal dispute between business tycoon Bernard Tapie and Credit Lyonnais, a bank partly owned by the government, to private arbitration. Critics have said she abused her position by referring the case to arbitration, since the bank was partly owned by taxpayers.
Tapie was awarded $400 million in the dispute, which revolved around the sale of sportswear company Adidas. Tapie was a major shareholder in Adidas and had lost his case in France's highest court, and was planning an appeal, when Lagarde stepped in and assigned the case to a private arbitrator.
Lagarde approved the $400 million settlement, which she said at the time was the "best solution" to the dispute.
She has denied any wrongdoing. Her attorney Yves Repiquet said Wednesday the search of her apartment would "contribute to the exoneration of my client of any criminal wrongdoing."
Lagarde replaced Dominique Strauss-Kahn as IMF director after he resigned in 2011 amid allegations he sexually assaulted a maid in a New York hotel. Charges in that case were later withdrawn.
Lagarde may have to resign the IMF job if investigators initiate a full inquiry, the Times said.