An ambulance took the Chip Ganassi Racing driver, who hails from Sweden, to the hospital after the wreck triggered by Takuma Sato on the first lap.
Sato, Ryan Hunter-Reay, James Hinchcliffe and Alexander Rossi were treated and released from the on-site medical center.
Sato, the 2017 Indianapolis 500 winner, said he thought he was all clear as he tried to make an aggressive pass early in the race.
“I’m not really over-aggressive,” he said.
Rosenqvist’s injuries weren’t considered life-threatening. IndyCar medical director Geoffrey Billows said Rosenqvist was walking and was expected to be fine.
Will Power won the shortened race, which was called with 72 laps left because of lightning and severe weather in the area.
Rosenqvist, 27, has been in motorsports for over 10 years.
Rosenqvist first found a home in a single seater in Asia in 2008 before moving on to Europe as a driver in the Formula 3 feeder series, where he won 13 races and the championship in 2015.
A year later, Rosenqvist found himself in the Indy Lights series, a step below Indy cars. Rosenqvist made a name for himself by winning three of the 10 events he started, and he made a crucial connection with the CGR team by testing for them at Mid-Ohio in 2016 and 2017.
Rosenqvist won a pair of races in Formula E a year ago before nabbing a highly coveted seat with Ganassi’s Indy program.
The Associated Press contributed to this report.