The SORA institute-led study found that 0.32 percent of those surveyed in the first week of April tested positive for the new coronavirus.
SORA said it was the first such study in the EU to better understand the virus's prevalence.
The result means some 28,500 of Austria's close to nine million people were likely affected, the institute said, compared to the official statistic of up to 12,200 coronavirus infections for that April week.
SORA said taking into account deviations, between 10,200 and 67,400 people in total could have been affected. The study surveyed 1,544 people.
“There has been the assumption that more people are infected than those officially tested… It's along the lines of other findings so far,” SORA founder Christoph Hofinger told AFP.
The Alpine nation adopted strict confinement measures in the middle of March, ordering people to largely stay at home, only allowing food shops and pharmacies to stay open and restricting people from entering the country.
As the increase in the number of new infections has flattened out, the government says smaller shops and gardening and hardware stores can re-open next week, as a first step in a gradual loosening of measures.
On Friday, Austria reported some 13,400 coronavirus infections with 319 deaths.