The probe affects about 393,000 cars from the 2006 through 2008 model years.
The National Highway Traffic Safety Administration says it has received six complaints of suspension failures, with three happening at highway speeds, according to documents posted on its website on Friday. The investigation was opened on March 25.
The agency says rust in the frame can cause control arm failures. A car's wheel hubs are attached to the control arms.
No crashes or injuries were reported but two of the failures activated the cars' electronic stability control systems.
Hyundai said in a statement Monday that it's too early to draw conclusions about the complaints and that no safety defect has been found. The automaker said it is cooperating with NHTSA and will take necessary action to ensure its customers' safety.
In one complaint from the Pittsburgh area, the owner of a 2006 Sonata said the rear of the car swerved while it was being driven, and the electronic stability control light came on. The owner took the car to a mechanic, who found that the rear frame was corroded and cracked on sides, causing the rear tires to wear prematurely. The frame, tires, lower control arms and other suspension parts were replaced on the car, which had almost 160,000 miles on it.
The agency says investigators will figure out if the problem is bad enough to cause a recall.
Hyundai spokesman Jim Trainor said in an e-mail that any customers with issues should take their cars to a Hyundai dealer.