The 21-year-old rookie was fortunate to escape serious injury after his Toro Rosso slammed into, and under, the energy absorbing Tecpro barriers at about 200kph in Saturday's session.
"My back and my neck are just a bit sore from the accident, but I'm totally ready," he said in a team statement.
"Hopefully tomorrow I will wake up in a good shape and maybe I can try and race -- this is definitely the intention."
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The accident ended practice and forced organisers to cancel a following GP3 race while extensive repairs were made to the barriers.
Toro Rosso initially said Sainz would be kept in hospital overnight but they issued a later statement to say he had been released.
Pictures of the scene showed tyre marks along the barrier on the outside of the track in the braking zone for the corner, suggesting Sainz made contact with the wall before reaching the run-off area.
Earlier, Sainz tweeted from his hospital bed that he is OK.
"I hope he will have a good night's sleep and tomorrow morning he will have to go through the FIA medical checks to decide if he will be able to take part in tomorrow's race," said team boss Franz Tost.
Separately, stewards agreed to a team request to allow Sainz to race providing he was passed fit.
Television images showed the Spaniard, strapped to a stretcher, giving a thumbs-up sign after being extracted from the wrecked car and taken to a waiting ambulance.
Replays showed the car snapping left and hitting a concrete wall, then skidding along in a cloud of debris at turn 13 with the front left wheel dangling on tethers in front of the driver.
"Is he OK? Because it looks like a big one," team mate Max Verstappen asked over the team radio as the medical car sped to the scene of the impact and the paddock collectively held its breath.
Tost said the fact the car went under the barriers was worrying and others expressed safety concerns about the installation of the barriers and the way the car had penetrated beneath them.
"I think we've definitely dodged a bullet there -- the car shouldn't have gone under the barriers, absolutely not," said Williams performance engineering head Rob Smedley.
"That isn't what's supposed to happen so that's disconcerting, to say the least, to watch."
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