The workers were paid an allowance for mileage, but were not paid for the time spent travelling.
This was a serious injustice for an already low paid job, he said.
Human Rights Commission Equal Opportunity Commissioner Judy McGregor has backed the union's claim.
The commission sought legal advice from law firm Russel McVeagh, which said there was a good argument that travel time between clients constituted work under the Minimum Wage Act, Mr Ryall said.
Health Minister Tony Ryall today issued a brief statement in response to the union filing its case with the Employment Relations Authority.
"This is a matter between home care employers and home care employees. We are aware different employers have different approaches, and we will be watching how the case progresses.''
