Its European operation expanded past year to include United Kingdom discount retailer Poundland.
The group said in a stock exchange announcement: "Steinhoff will update the market as the aforesaid investigation proceeds".
Steinhoff said chief executive Markus Jooste, who had been at the helm for almost 20 years and oversaw its expansion to one of the world's largest household goods retailers, had resigned with immediate effect and consultants PwC would undertake an "independent investigation".
The company has also postponed its full year results as it calls in accountants from PwC to launch an independent probe into the accounting irregularities.
The development had wider repurcussions too, with the chief executive of Steinhoff African Retail (STAR), part of Steinhoff which includes the control of Shoprite, also resigning on Wednesday and its shares falling 21.5 percent to 19.30 rand by 0855 GMT. It warned it might have to restate financial statements from prior years. In the United Kingdom, along with Poundland it also owns Bensons for Beds and Harveys. Steinhoff derives about 60% of its earnings in Europe and 34% in Africa.
South African billionaire and chairperson of the company, Christo Wiese, will run the company on a temporary basis.
Mr Jooste had been in charge for close to two decades and oversaw Steinhoff's expansion from a furniture manufacturer in South Africa to one of the biggest global household goods retailers.
Martin Jooste announced his resignation with immediate effect late last night, as the company announced that "new information has come to light" relating to "accounting irregularities requiring further investigation".
Kepler Cheuvreux said the pending tax and accounting investigations "could show severe irregularities".
It is unclear what accounting irregularities the company was referring to in its statement on Wednesday.