The employees of PrimeFlight transport disabled passengers throughout the airport.
At a news conference Monday, they said the wheelchairs often have bad brakes, broken handle grips or other problems.
They also say workers have not been properly trained to aid passengers with disabilities, including helping them to use the bathroom.
The local chapter of Service Employees International Union filed complaints with two federal agencies last week on the workers' behalf.
A spokeswoman with the Occupational Safety and Health Administration says the agency has begun investigating.
A representative of Tennessee-based PrimeFlight did not immediately return a request for comment.