The investigation will concentrate on the suspicion of fraud committed through the sale of vehicles with manipulated emissions data, and aims to determine who was responsible, prosecutors in Braunschweig said in a statement.
In the German system, anyone can file a criminal complaint with prosecutors, who are then obliged to examine them and decide whether there is enough evidence to open a formal investigation.
In this case, following the revelations about the rigged tests, prosecutors in Braunschweig, near VW's headquarters in Wolfsburg, received about a dozen complaints, including one from Volkswagen itself, said spokeswoman Julia Meyer.
She said it was too early to say if and when prosecutors may try and interview Winterkorn himself, and that she did not know whether he already had an attorney to represent him.
She said at this stage, she could not estimate how long the investigation would last.
"This is a very broad case and in other such investigations it has taken many months, sometimes years," she said.
Winterkorn, Volkswagen's CEO since 2007, resigned Wednesday — days after the world's top-selling carmaker admitted that it had rigged diesel emissions to pass U.S. tests during his tenure. He said that he was going "in the interests of the company even though I am not aware of any wrongdoing on my part."
Under German law, it is not possible to bring charges against a company — only against individuals. Meyer would not elaborate on specifics of the investigation, and it wasn't clear what Winterkorn's suspected role might be.
The head of VW's Porsche division, Matthias Mueller, was appointed Friday as his successor.
The company has admitted that it used a piece of engine software to cheat on diesel car emissions tests in the U.S. It will have to fix programming it has said is in some 11 million cars worldwide, far more than the 482,000 originally identified by U.S. authorities.
Details on what cars are involved have emerged gradually. The group, which has 12 marques in all, said Friday that some 5 million cars made by its core Volkswagen brand had the diesel engine in question.
On Monday, Audi said that 2.1 million of its vehicles also had the engine.
Volkswagen shares were down 6.5 per cent in midday Frankfurt trading at 108 euros ($120.87).