The car parts maker is one of the manufacturers under investigation on suspicion of hiding illegal levels of pollution following a regulatory clampdown on toxic fumes triggered by Volkswagen's 2015 admission that it had cheated emissions tests.
The software used in the 1.6 litre diesel engine Volkswagen developed for sale in Europe came from Continental, though the supplier has said it was not involved in the manipulation as engine controls are programmed by clients themselves.
The individuals now under investigation are suspected of breach of trust, failure to fulfil supervisory duties and being an accessory to fraud, the Hanover prosecutor's office said on Thursday.
The people under investigation also include a former board member of Continental's Powertrain unit and two employees below board level, prosecutors said, without naming the persons.
"This development shook us," Continental's works council said in a statement.
"We at Continental are paying dearly for the focus on profit at any price. Therefore, we call for a return to what the company stands for: trust, reliability, transparency and openness. We demand a new start with more courage to be honest," it said.
Continental, Degenhart and Schaefer declined to comment.
Shares in Continental were down 3.3% by 1145 GMT.
Continental said late on Wednesday dismiss its Chief Financial Officer Wolfgang Schaefer it would replace Schaefer as finance chief, and that Chief Executive Nikolai Setzer would take over his responsibilities for now.
The investigators had already searched Continental's compliance department in Frankfurt and a private residence that was not Schaefer's flat earlier in November, a spokesperson for the authorities said on Thursday.
(Reporting by Jan Schwartz; Writing by Zuzanna Szymanska; Editing by Maria Sheahan and Steve Orlofsky)