The man was suspected of leaking the highly sensitive and confidential document.
He was arrested on Tuesday but has been found hanged in his police cell.
Swiss prosecutors said there was no indication of a third party being involved in his death.
Schumacher, 45, suffered life-threatening head injuries in December after a horrific ski accident in the French resort of Meribel.
He was treated in Grenoble Hospital until June 16 when he was transferred to University Hospital Lausanne in Switzerland.
He was taken by ambulance but Rega, a Swiss helicopter company, was also sent Schumacher's medical dossier when helicopter transport was being considered.
It is believed the man who was yesterday arrested was a manager at Rega.
European media was offered Schuamcher's medical file for 60,000 Swiss Francs.
It contained detailed information about his treatment since his accident.
French prosecutors launched a criminal investigation into the alleged theft.
A statement made by Zurich police read: "A man arrested following the theft of Michael Schumacher's records was found hanged in his Zurich police prison cell.
"Based on findings by the investigators, there was no intervention by a third party in this case."
Seven-time F1 champion Schumacher, 45, suffered serious brain injuries in a skiing accident in the French Alps on December 29 and was not expected to last the night because his injuries were so severe.
He underwent two emergency operations within 24 hours and his life hung in the balance for weeks.
He was discharged from hospital in June and is now in a rehabiliation clinic in Lausanne, not far from his £35 million pound mansion home.
A brief statement from Zurich prosecutors today said: "A man has been found on the morning of Wednesday 6 August 2014 hanged in his cell in the Zurich jail.
"There are no references to third-party influence according to the recent findings of the Zurich Canton Police Department and the public prosecutor's Office.
"The deceased was arrested in connection with the transfer of medical records by Michael Schumacher on the 5th August 2014."
It was as an officer checked on him shortly after 7.00am that his body was discovered.
Ernst Kohler, CEO and Chairman of the executive board of Rega, said: "We are all deeply affected.
"We know that this member of Rega staff was yesterday taken on suspicion of violation of professional secrecy into police custody and allegedly committed suicide in the night.
"This tragic event makes us sad and speechless.
"Our thoughts and sincere condolences are at this very moment with the relatives of the deceased and the people close to him."