Swiss broadcaster RTS reported that Schumacher, 45, was transferred to the Lausanne university hospital (CHUV) on Monday from Grenoble, France.
"Mr. Schumacher was taken in charge by CHUV this morning," Darcy Christen, a spokesman from the hospital, is quoted by RTS as saying.
"His family is with him, in a space specially fitted out to preserve their privacy and to ensure the best possible care," Christen said.
The Lausanne hospital declined to give further information "out of respect for medical confidentiality and the private sphere of the family".
Kehm did not say where the German seven-time Formula One racing champion was taken and did not reveal his condition.
“For the future we ask for understanding that his further rehabilitation will take place away from the public eye.”
According to German tabloid Bild, Schumacher has been able to communicate with his wife Corinna and their children.
In March, reports indicated that Corinna Schumacher was building a 15-million-franc ($16.7-million) medical suite at the couple’s mansion overlooking Lake Geneva in Gland in the canton of Vaud.
The sprawling estate is 32 kilometres west of Lausanne.
Doctors put Schumacher in a medically induced coma on January 30th in the CHU hospital in Grenoble.
He was transferred there for treatment of serious head injures suffered from a December 29th accident while skiing off-piste in the resort of Méribel in the French Alps.
Schumacher underwent two operations in the days after the accident to remove life-threatening blood clots on his brain.