The Pole will miss the start of the season and almost certainly all of the forthcoming 2011 schedule, but the early signs are good that he will make a recovery despite earlier fears he might lose his right hand.
However, a statement issued by his F1 team Lotus-Renault said "it will be several days before it is known if the (hand) operation has been 100 per cent successful"
Kubica, 26, was put back to sleep on Monday, while doctors considered further surgery to treat elbow and shoulder fractures.
He also has leg fractures.
"Kubica is conscious," said an intensive care spokesman at the Santa Corona hospital. "The first thing he thought about was his co driver and was informed about his condition."
The spokesman added that Kubica "lost a lot of blood" in the accident and had been "critical" but is now stable.