Wilson's car was apparently out of control after being hit by the debris and veered into the wall at the Pocono Raceway in Pennsylvania.
His Andretti Autosport team mate Ryan Hunter-Reay, who went on to win the 500-mile (804.67 km) race, said he had not heard of the Briton's condition in hospital though he had been unconscious at the track.
"All I know is that he was unconscious," Hunter-Reay said.
"He was not responding. He was airlifted. That's all obviously very bad details."
Wilson's crash was reminiscent of a 2009 incident when Brazil's Felipe Massa was struck in the helmet by a spring from Rubens Barichello's car during qualifying for the Hungarian Grand Prix and had to undergo surgery.
(Reporting by Lewis Franck in Charlotte, North Carolina; Editing by Frank Pingue/Greg Stutchbury)
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