Kehm urged journalists to respect the 44-year-old German's privacy after security guards said they intercepted a reporter disguised as a priest trying to get into Schumacher's room.
"Security got him before he came close ... I don't want to go into details of what exactly we are doing security-wise. However I can assure you there is security because we do have constant attempts from media and people to come close," she said.
Schumacher is battling for his life after slamming his head against a rock while skiing off-piste in the French resort of Meribel on Sunday.
"His condition remains stable this morning. At the moment this is good news but I don't want to go into further prospects as it is too early. He is still in an artificial coma," Kehm said at the hospital in the eastern city of Grenoble.
She added the "situation remained critical" and declined to comment on his recovery prospects. Doctors carried out an operation on Monday to alleviate the build-up of pressure in Schumacher's skull as a result of internal bleeding.
Schumacher's accident triggered an outpouring of concern among fans, former team-mates and rivals around the world. German Chancellor Angela Merkel expressed her shock and hopes for a recovery.
Schumacher's wife Corinna and teenage children Mick and Gina-Marie are at his bedside and he has received visits from his retired motor racing brother Ralf and close friends.
"They have the possibility to see him and be close to him so that is nice. There is always someone with him," said Kehm.
Schumacher, who is due to turn 45 on Friday, is the most successful Formula One driver of all times with a record 91 race victories in a career spanning more than two decades.
He left the sport last year after a less successful three-year comeback with Mercedes following an earlier retirement from Ferrari at the end of 2006.