Nissan Motors said the violations were discovered during an investigation over several months that was instigated by a whistleblower. Brazilian-born Carlos Ghosn, 64, also allegedly engaged in personal use of company assets, it said.
Nissan said it was providing information to the prosecutors and cooperating with their investigation. The allegations also concern another Nissan executive, its representative director Greg Kelly.
Japanese media said Ghosn voluntarily submitted to questioning by Tokyo prosecutors on Monday.
Nissan's CEO Hiroto Saikawa planned to propose to its board that Ghosn and Kelly both be removed from their posts.
"Nissan deeply apologizes for causing great concern to our shareholders and stakeholders. We will continue our work to identify our governance and compliance issues, and to take appropriate measures," the company said in a statement.
The allegations are a serious blow at a time when Nissan and another alliance member, Mitsubishi Motor Co., are still overcoming scandals over their quality testing reporting.
Ghosn is credited with helping engineer a remarkable turnaround at Nissan over the past two decades, resuscitating the Japanese automaker from near bankruptcy after he was sent in by alliance partner Renault SA of France.
He served as Nissan's chief executive from 2001 until April 2017, becoming chief executive of Renault in 2005, leading the two major automakers simultaneously. In 2016, Ghosn became Mitsubishi Motors' chairman.
The Nissan-Renault-Mitsubishi group is among the biggest auto alliances in the world, selling about 10 million vehicles a year. Before joining Renault, Ghosn worked for Michelin North America.
For the past two decades, he has maintained an unusually high profile in a nation where foreign chief executives of major Japanese companies are still relatively rare.
Ghosn has appeared on magazine covers dressed in kimono, vowing to renew the Nissan brand. He was widely praised in Japanese industry circles for delivering sorely needed cost cuts and introducing greater efficiency at a time when Nissan needed a fresh start.