Tapie, who can be held for up to four days without charge, was to be questioned over a €400-million state payout he received in 2008 when Lagarde was France's finance minister.
A combative Tapie played down the procedure.
"I don't give a damn," he told Europe 1 radio earlier Monday. "I'm not worried. I cannot imagine what they could find."
The cash payout to Tapie, who served a prison sentence for match-fixing during his time as the president of France's biggest football club, Olympique de Marseille, related to a dispute between the businessman and partly state-owned bank Credit Lyonnais over his 1993 sale of sports group Adidas.
Tapie claimed that Credit Lyonnais had defrauded him by intentionally undervaluing Adidas at the time of the sale and that the state, as the bank's principal shareholder, should compensate him.
Lagarde was responsible for referring the issue to a three-man arbitration panel, which ruled in Tapie's favour.
Three people have been charged over the scandal since May, including Stéphane Richard, the head of telecommunications giant Orange, for organised fraud.
The company's board has however voted to let Richard remain boss and French President François Hollande has expressed strong backing for him. The French state is a major shareholder in Orange.
Richard was Lagarde's chief of staff when, in 2008, she sanctioned the payout to Tapie.
Lagarde is suspected of having rigged the process that led to the payout, thus ensuring that Tapie would get the cash in return for supporting her boss, Nicolas Sarkozy, in his successful 2007 presidential election campaign.
A source close to the investigation said Richard told them that Tapie was present at a meeting at the Elysee palace in 2007.
The IMF chief was questioned for two days in May about her role in the affair.
She was not placed under formal investigation – the French equivalent of being charged in other legal systems – but she remains what is termed an "assisted witness", which means judges can summon her for further interrogation at any time.
One member of the arbitration panel, Pierre Estoup, 86, was placed under formal investigation on the same charge as Richard.
Also charged on the same count was Jean-Francois Rocchi, former president of the CDR, an ad hoc structure created by the state in 1995 to settle the debt of the then-struggling Credit Lyonnais bank, which dealt with Tapie during the legal dispute and through whom the cash payout was made.
The International Monetary Fund's executive board has repeatedly expressed confidence in Lagarde and said there is no reason for her to step aside from her duties while the corruption case is being concluded.
That stance will inevitably be tested should Lagarde be placed under formal investigation.
Critics of Lagarde's decision to send the Tapie case to arbitration say that, even if there was no shady motive, she should not have run the risk of the state being forced to pay compensation to a convicted criminal who was bankrupt at the time.
Lagarde has always maintained that she acted in the best public interest and her supporters have pointed out that she had inherited the arbitration idea from her predecessor at the finance ministry.