Peter Horton said Rick Hendrick and his wife, Linda, were taken to Lower Keys Medical Center Monday night with injuries that appeared to be non life-threatening, The Miami Herald reported.
Horton said the pilot and co-pilot of the Gulfstream 150 had radioed to the tower that the aircraft had "no brakes."
It skidded completely off the runway and came to a stop along an unpaved safety area that had just been added in May.
Horton said the pilot and co-pilot, whose names were not immediately available, did not appear to be injured but were taken to the hospital for evaluation.
The plane was registered to NASCAR's five-time champion Jimmy Johnson who drives for Hendrick.
The National Transportation Safety Board will investigate the accident.