By some estimates, the lawsuit could cost Volkswagen $10 billion if the shareholders prove in court that top managers knew of the illegal behavior sooner than they have admitted.
The suits also threaten the Porsche and Piëch families, descendants of Ferdinand Porsche, inventor of the Volkswagen Beetle. The families’ wealth is tied up in Porsche Automobil Holding.
Volkswagen has already agreed to pay criminal and civil penalties of $4.3 billion under the terms of a plea agreement with American authorities, a piece of the overall $22 billion in settlements and fines in the United States. Six executives have so far been charged in the United States, and one engineer has pleaded guilty to conspiring to defraud regulators and car owners.
On Wednesday, prosecutors said they were investigating whether Mr. Müller improperly withheld information about the emissions scandal from shareholders of Porsche Automobil Holding before news of the deception became public in September 2015.
In a statement, Stuttgart prosecutors said that Mr. Müller, Mr. Winterkorn and Mr. Pötsch were suspected of “knowingly failing to communicate in time the consequences arising from manipulation of software in Volkswagen diesel vehicles, especially financial consequences for Porsche S.E.”
In addition to his duties at Volkswagen, Mr. Müller is a member of Porsche Automobil Holding’s management board. Mr. Pötsch is also a member of the holding company’s management board and Mr. Winterkorn is a former member. The holding company is controlled by members of the Porsche and Piëch families, but it is subject to stock market regulation because it also has publicly traded preferred shares which do not have voting rights but are entitled to dividends.
“Porsche S.E. considers the accusations to be groundless,” the company said in a statement, adding that it “has properly fulfilled its disclosure obligations under capital markets law.”
Mr. Pötsch and Mr. Winterkorn had already been identified in a related investigation into market manipulation involving Volkswagen shares. Mr. Müller has not been identified as a suspect in that inquiry, which is being conducted by prosecutors in Braunschweig, near the Volkswagen headquarters in Wolfsburg, in northern Germany.
Herbert Diess, a member of the Volkswagen management board in charge of cars made under the Volkswagen brand, has also been named as a suspect in the Braunschweig market manipulation case.
Mr. Winterkorn resigned as chief executive of Volkswagen in September 2015, after the Environmental Protection Agency in Washington accused the company of using engine software to conceal excess emissions by diesel cars. He was replaced by Mr. Müller, a longtime Volkswagen executive who had previously been in charge of the Porsche sports car division.
Volkswagen declined to comment, but it repeated assertions that the company’s executives had fulfilled their duties to shareholders.
Scrutiny of Volkswagen’s management board had already been intensifying.
In January, German prosecutors said that Mr. Winterkorn was a suspect in a criminal investigation into the emissions cheating. Mr. Winterkorn has testified in the German Parliament that he did not learn of the illegal software until shortly before it was disclosed by the E.P.A. in September 2015.
German investigators searched the offices of Mr. Müller and Rupert Stadler, the chief executive of the Audi luxury car unit who is also a member of Volkswagen’s management board, in March. The investigators took documents and other materials while not naming either man as a suspect. Both have denied any wrongdoing.
So far, the Volkswagen supervisory board, a group of shareholder and worker representatives who oversee the management board, has resisted calls for deeper changes in top management. The Porsche and Piëch families, which, via the holding company, own a majority of Volkswagen shares with voting rights and exert strong influence over the supervisory board, have also maintained their backing of the management.