The allegations involve alleged kickbacks and bribes worth millions of euros in connection with arms deals in South Korea, according to the prosecutors in the company's home state of Baden-Württemberg.
A Tognum board member who had some responsibility for Asian business functions is being specifically investigated, prosecutors told the DPA news agency.
Tognum had hired accounting firm Ernst & Young to examine business irregularities it said it had identified in its subsidiary MTU Asia. The 200-page report is now before public prosecutors and has obviously been deemed credible enough to open the criminal investigation.
Bloomberg News said the report described parties involving South Korean defence officials at red-light district nightclubs.
A company spokesman said that the supervisory board would meet on Tuesday to discuss the situation.
Tognum builds engines for boats, tanks and locomotives as well as emergency generators. It was recently taken over by a joint venture between Daimler and Rolls Royce, and is currently in the process of being integrated into that new business.