The National Highway Traffic Safety Administration says a fastener can come loose, causing the steering shaft to come part and drivers to lose control of the vehicle.
The investigation covers about 70,000 Santa Fes from the 2011 model year. It will determine if the problem is bad enough for Hyundai to recall the SUVs.
No injuries or crashes have been reported.
NHTSA says one driver complained about a complete loss of steering. Hyundai also got a complaint that a loose bolt caused a similar problem.