Conway had surgery for multiple fractures in his lower left leg and has been diagnosed with a compression fracture in his back. The back injury was not confirmed until Monday morning.
Conway's team, Dreyer & Reinbold, has yet to say who will replace him in the No. 24 car.
The 26-year-old Englishman was injured on Lap 199 when Ryan Hunter-Reay's car, already low on fuel, started sputtering. Conway was going about 220 mph through the short chute between turns three and four, and couldn't avoid running into the back of Hunter-Reay. The contact sent Conway airborne and into the catch fence, splitting the car into two large pieces though the driver's seat remained intact.
He was airlifted to a local hospital after the race, where he had surgery.
On Monday morning, race winner Dario Franchitti reflected on the horrific crash as he took a lap with reporters in a van.
"When they called yellow, there was relief, like 'OK, this helps us.' Then, the next thing you heard was 'Debris is everywhere,'" Franchitti said. "And I thought 'Oh no.' Then I saw it was Mike and was hoping it was OK, and when I came around the next time, I saw his helmet was off and I knew he was OK. When you see the size of that accident, you knew he was lucky."
Conway will be fitted for a back brace that he will wear for three months.
Hunter-Reay injured his left thumb Sunday but not in the big accident that forced the race to finish under caution.
He was scheduled to have surgery Monday and will be fitted with a carbon fiber splint.
Doctors believe the splint will allow Hunter-Reay to compete Saturday at Texas in what could be his final race under the Andretti Autosport banner. His part-time deal was set to end after Texas.
Hunter-Reay, who has one win this season, finished 18th at Indy. Conway was 19th.
Dreyer & Reinbold had three other drivers in Sunday's race — Brazil's Ana Beatriz, South Africa's Tomas Scheckter and England's Justin Wilson. Wilson and Conway, also a Brit, are the team's two full-time drivers.