Bowman, who turned 30 this week, was competing in the Limit Sprint Car Series at 34 Raceway in Iowa when the crash occurred.
He flipped multiple times after colliding with Conner Morrell, and suffered a compression fracture of a vertebra.
Hendrick Motorsports expects him to be out of action for three to four weeks.
He is not the first HMS driver sidelined by an injury this year, as Chase Elliott missed six races after suffering a fractured tibia in his left leg while snowboarding in March.
NASCAR Xfinity Series regular Josh Berry filled in on ovals for Elliott, and he will do the same for Bowman in the coming weeks. While subbing for Elliott, he finished as high as second at Richmond Raceway.
Bowman is currently winless and sits ninth in the championship standings. He was leading the regular season points before a violation on the No. 48 car cost him 60 driver and owner points.
The team will request a medical waiver, so that he may remain eligible for the playoffs.
“We’re relieved Alex is home, in good spirits and getting world-class treatment,” said Rick Hendrick, owner of Hendrick Motorsports.
“Giving him ample time and the foremost resources to heal is our top priority.
“He’s having a tremendous season, and the No. 48 is at the top of its game.
“We know what Josh is capable of in the race car and that Blake [Harris, crew chief] and the team will continue operating at a high level until Alex is ready to return. He has our full, unequivocal support.”
This isn't the first time Bowman has been sidelined for medical reasons. He missed five races at the end of the 2022 season after suffering a concussion in a crash at Texas.
In a statement, he said: “Last night I was involved in an on-track incident while racing and fractured a vertebra.
“First, I want to let everyone know I'm feeling OK. My focus is now on healing and resting.
“Being out of the car is never an update any driver wants to make.
“I'm thankful to Josh Berry and Hendrick Motorsports for stepping up to the plate and I know the entire Ally Racing team will give it their all these next few weeks.
“I'll be doing everything I can at home to help the team and ensure my recovery is as quick as possible to get back in the 48 car soon.”