The German journalists association, or Deutsche Journalisten-Verband, is also warning against the publication of the information, arguing it is "without substance and relevance".
"The contents of this file has neither political nor social significance and would be a completely unacceptable and very serious interference with the personal rights of Michael Schumacher," chief Michael Konken added.
Germany's Welt newspaper now reports that the university hospital in Grenoble reported to police the theft and breach of patient confidentiality last Thursday.
Days earlier, Schumacher, 45, had been transferred by ambulance from intensive care at Grenoble to a rehabilitation hospital in Lausanne, Switzerland.
The French news agency AFP has further details. It claims the 'medical file' is in pact a multiple-page doctor's summary of Schumacher's case copied from the hospital's computer system.
The report said the hospital is not sure whether an employee stole the dossier or if it had been the victim of 'hackers'.
"An individual, communicating by email, is asking for 60,000 Swiss francs to provide a document of several dozen pages that summarises everything that happened at Grenoble during Schumacher's hospitalisation," local prosecutor Jean-Yves Coquillat said.
Hospital director Jacqueline Hubert told Bild newspaper that employees of the hospital with potential access to the file have been interviewed by police.
"This is a limited number of people," she said. "Michael Schumacher's information was saved under a false name in the system."
Meanwhile, the hospital currently treating Schumacher in Lausanne insists it is taking all measures to protect the former F1 driver's privacy.
"We have the highest standards for all of our patients," spokesman Darcy Christen told Welt. "Our data is protected by a very secure system."