The German driver, who suffered severe head injuries in a ski accident in the French Alps in December, was transferred from Grenoble in France to a Swiss medical centre on June 16.
"For several days stolen documents and data have been offered for sale," Sabine Kehm, managing director of Michael Schumacher's offices in Geneva, said in a statement on Monday.
"The offeror claims them to be the medical files of Michael Schumacher. We cannot judge if these documents are authentic.
"However, the documents are clearly stolen. The theft has been reported. The authorities are involved," added Kehm.
Criminal charges and damages would be sought against anyone involved in the illegal sale or publication of his confidential records, she said.
A spokeswoman for the University Hospital of Lausanne (CHUV) in western Switzerland, where the German is being treated in the neurological rehabilitation unit, said she had "no comment" on the case.
The centre treated former Zairean dictator Mobutu Sese Seko for cancer in the mid-1990s and last year its forensic scientists analysed the remains of the late Palestinian leader Yasser Arafat for traces of poison.
Schumacher, the most successful Formula One driver of all time, has had several brain operations since his accident in the resort of Meribel.
His wife Corinna and two teenage children live in the family home midway between Geneva and Lausanne.
(Reporting by Stephanie Nebehay, editing by Tony Jimenez)
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