Anglicare looked at 45,992 rental listings across the country and found just 712, or two per cent, could be afforded by people on the minimum wage.
In SA only two of 1125 properties listed were considered appropriate and affordable for a single person.
"Rental prices are skyrocketing out of control," SA Greens housing spokesman Robert Simms said.
"While many South Australians are being locked out of the rental market, some landlords are making record profits.
"It's time for the state government to follow the lead of other jurisdictions overseas and implement rent controls to protect struggling renters.
"This has worked in New York for years - why not Adelaide?"
Mr Simms said he would raise the issue when parliament resumed next week.
The Greens also renewed calls for the government to boost investment in public housing to reduce prices.
At a federal level, the party said it would push for 70,000 affordable homes to be built across Adelaide and regional South Australia.
It said the plan would ensure low-income earners were not priced out of the housing market, with options for low-cost and long-term secure rentals and purchase options at around $300,000.
SA Senate candidate Barbara Pocock said the housing market was particularly brutal for low-income earners.
"For a person working full time on minimum wage in Adelaide, almost no rentals are affordable," she said.
"The same goes for those on income support, whether that be Youth Allowance, JobSeeker or the disability and age pensions."
Sitting SA Senator Sarah Hanson-Young said it was a disgrace that so many Australians could not afford basic housing.
"Housing is a basic human right. When everyday South Australians cannot afford to put food on the table and keep a roof over their heads, there is a serious problem with the system," she said.
