Felipe Massa has successfully undergone surgery for the injuries he suffered in his accident in qualifying in Hungary.
Ferrari said the driver will now remain under observation in the intensive care unit at the AEK hospital in Budapest, where the Brazilian was taken after being hit by a spring during Q2.
Massa had suffered a damaged skull and brain concussion, as well as a cut on his forehead.
The Italian team said a further update on his condition will be issued tomorrow morning.
Brawn confirmed the spring belonged to a damper from Rubens Barrichello's Brawn car, weighing around 800 grams.
"We had a problem at the back, so we are still investigating and we haven't had the piece back from the FIA yet so once we get it back we can understand what occurred and then draw some conclusions," said team boss Ross Brawn.
"It is the first time we've had a problem with the car. The car has been really reliable and we are obviously looking all through the data to understand what caused the problem. It is hard to comment at the moment until we have studied everything.
"We put a new component on Jenson's car in qualifying just to be safe, but we are still studying everything that went on to understand what happened."