James Hinchcliffe was stable in hospital on Tuesday after he was involved in the fourth dramatic crash in less than a week at the Indy 500.
The Canadian, 28, was hurt when part of his car's suspension pierced both of his legs after he hit a wall.
His Schmidt Peterson Motorsports team boss Sam Schmidt praised the emergency response to Monday's crash.
"People went completely above and beyond," he said. "We're relieved that James is awake and out of surgery."
On Wednesday, Helio Castroneves's car went airborne after the Brazilian hit the perimeter wall during practice for the 500-mile race on 24 May.
Fellow Chevrolet driver Josef Newgarden lost control of his car 24 hours later going into the first turn, flipping after also hitting the wall.
CFH Racing driver Ed Carpenter was unhurt after his car crashed into a wall and flipped over on Sunday.
Rule changes have been introduced amid concerns over the cars' designs.
In an effort to reduce speed and increase downforce, the cars - which can travel at up to 230mph - must now run race-level aerodynamics and engine-boost settings during qualifying.