Daytona International Speedway President Joie Chitwood told the Los Angeles Times 14 of the injured were hospitalized and 14 others were treated at the Florida track following the fiery crash in the final lap of the Nationwide Series event.
Of the seven of victims admitted to Halifax Medical Center in Daytona Beach, two were in critical condition, including a child, hospital spokesman Byron Cogdell told USA Today.
The adult in critical condition was suffering from head trauma, he added.
Daytona Beach Police Public Information Officer Jimmie Flynt told the newspaper six other victims were taken to Halifax Urgent Care in Port Orange for minor injuries.
One person went to Florida Memorial Hospital for minor injuries, he said.
The fiery wreck happened during the final turn of the race, when Kyle Larson's car flew into a catch fence that divides the track from the seats.
The front end of Larson's car broke into pieces, with parts of it piercing the fence.
Some of the debris hit a spectator 45 rows up in the stands while other car parts -- included a tire -- also flew into the stands, the Sentinel reported.
Larson walked away from the crash and no other drivers were reported injured.
Fans could be seen lying down in the grandstand area after the crash.
Video showed fans being placed stretchers, with one woman's leg bleeding as she was carried away.
"You've been able to see and explain," NASCAR President Mike Helton told ESPN. "There was some intrusion into the fence and there were plenty of emergency worker ready to go and jumped right into it quickly."
Steve O'Donnell, NASCAR's senior vice president for racing operations, told the Times the damage to the fence should be repaired in time for Sunday's Daytona 500 Sprint Cup season opener.