Last year's overall championship runner-up was in intensive care after being hit on the head by bouncing debris from compatriot Rubens Barrichello's [ Images ] Brawn during Saturday's qualifying.
"After undergoing an operation yesterday afternoon, Felipe Massa's condition remains stable and there were no further complications through the night," Ferrari [ Images ] said in a statement.
"He will be given a CT scan today, which will provide more precise information."
Massa underwent emergency surgery at Budapest's AEK military hospital on Saturday, with a Defence Ministry official saying the driver had been in a "serious, life-threatening condition" before the operation.
The accident, which ruled Massa out of Sunday's race at the Hungaroring, brought back grim memories of the crash that killed compatriot and triple champion Ayrton Senna at Imola in 1994 and led to renewed concerns about safety.