"Michael's condition has been stable throughout the night," Kehm told reporters outside Grenoble's university hospital.
"There have been no significant changes. It is good news, but only for the moment. The situation remains critical."
Kehm said the record-holding F1 champion, who turns 45 on Friday,"has been carefully supervised throughout the night" and that his family remains with him.
She declined to give a prognosis and added that no further statements from her or doctors were planned for the day unless there are "significant changes."
Schumacher, who won a record seven F1 world titles and retired from the sport for a second time in 2012, fell and hit his head on a rock while skiing at the Meribel resort Sunday.
He underwent emergency surgery and was put into an induced coma. His condition later slightly improved, which allowed doctors to carry out a second operation late Monday to reduce pressure on the brain.
Gerard Saillant, who operated on Schumacher for a broken leg after a crash at the 1999 British Grand Prix and came to Grenoble as "a friend," said Tuesday that Schumacher still has lesions on the brain that require medical attention.
"These lesions need to be kept in check. We need to check on these every hour," he said.
Kehm Tuesday dismissed suggestions that Schumacher had been skiing fast before the accident and said that he had been on the slope with a few friends, not his son. She told reporters it appeared that he helped a friend who had fallen and then skied on, hit a stone while attempting a turn and then crashed head-on against a rock.
Schumacher's former Ferrari team and world football supremo Joseph Blatter were among many who included the racer in their New Year messages Wednesday.
"Happy New Year! Michael Schumacher ... we're all with you!," tweeted Ferrari, with whom the German won five straight world titles between 2000 and 2004.
FIFA president Joseph Blatter tweeted: "My thoughts are with Michael Schumacher & his family at start of 2014. Like many sports fans, I wait for positive news, & send him strength."