The Argentine-born former Spain international was in a stable condition having fractured bones in his shoulder and back, and punctured a lung, when his car left the road on Tuesday.
The club said surgery may be needed and that the player would not be available to start pre-season training with the rest of the squad, when they return to work on Saturday.
Atletico sports director Jesus Garcia Pitarch spoke of the accident at the presentation of defender Juanito and also touched on the futures of midfielders Maxi Rodriguez and Jose Antonio Reyes.
Argentina international Maxi, who has one year left on his contract, has been linked with a move away from the Calderon.
"We have decided not to extend his contract, but we have not listened to any of the offers that have arrived for him," Garcia Pitarch said.
Reyes spent last season on loan with Benfica and the Portuguese club had an option to buy him at the end of the deal.
"Reyes will be with us," he said. "Benfica have systematically failed to stick to their promises. They kept saying at the end of the week they would exercise the option to buy him, but it hasn't happened.
"If he repeats the season he had in Portugal we will be happy to have him with us. He knows he has to improve."
Atletico are in the Champions League play-off round next month after finishing fourth in the Primera Liga last season.
