Juan Manuel Correa is in an induced coma in a London hospital after suffering complications following the crash in which Anthoine Hubert was killed at last weekend's Belgian Grand Prix.
The Ecuadorian-American racing driver is in a "critical but stable" condition, his parents said in a statement on Saturday.
Correa, 22, broke his legs and suffered a spinal injury last Saturday when he crashed with Hubert during a Formula Two race at the Spa-Francorchamps circuit.
Frenchman Hubert, 20, died at the circuit 90 minutes after the race.
Correa, grandson of former Ecuador president Rodrigo Borja, was moved to London from a Belgian hospital, where he underwent four hours surgery last Sunday, on Tuesday.
In their statement, Juan Carlos and Maria Correa said: "New complications have surfaced as a consequence of the massive impact he suffered Saturday in Belgium.
"On his arrival to London, Juan Manuel was diagnosed with Acute Respiratory Distress Syndrome. This is an injury considered common in high impact accidents such as this one."