The percentage of people in Scotland who have been exposed to coronavirus is likely to be less than 5%.
Based on random testing of blood samples between 20 April and the end of June it was revealed that 4.3% had antibodies.
Researchers looked for the specific proteins that the body produces to fight infection.
The 4,751 samples tested came from routine blood checks carried out by the health service in Scotland.
Deputy Chief Medical Officer Dr Nicola Steedman presented the findings from Public Health Scotland during the Scottish government's daily briefing on Thursday.
She said the research was part of an effort to find out the "true number" of infections in Scotland - and to estimate the extent the virus had spread around the country.
The current number of confirmed cases in Scotland is 18,384, but Dr Steedman said this represented a small proportion of the total infections as many people displayed very mild symptoms, or had none at all.
"Generally when you hear the positive testing numbers here that we tell you about every day, this is mostly in those people who've been tested for coronavirus because they have symptoms," she said.
"So if you think about coronavirus in Scotland as an iceberg in the water then these positives are like the top of that iceberg that we can see above the waterline."
Coronavirus in Scotland: How many cases are there?
The population of Scotland is estimated to be 5,463,300, meaning that about 235,000 people in Scotland will have been exposed to Covid-19, according to this research.
This represents about 13 infections for every confirmed case.
235,000Estimated total infections
18,384confirmed cases following test
13estimated infections for each confirmed case
Researchers tested blood samples that were originally collected for other clinical reasons from labs in six NHS health boards: Greater Glasgow and Clyde, Grampian, Highland, Lanarkshire, Lothian, and Tayside.
About 500 samples were collected each week.
Researchers said that the proportion of the samples with Covid-19 antibodies varied between 1.9% and 6.8%.
The report added: "Across these weeks, we can be 95% confident that the value lies between under 1% and 10%."
In an appeal to the public about complying with the current restrictions, Dr Steedman said: "Only a fairly small proportion of the population have so far likely been exposed to coronavirus in Scotland. And it is this low number of people, likely exposed, that explains and reinforces our on-going messages to you.
"Firstly, that we need to be careful when we are easing out of lockdown and secondly this is why we still want you to follow all of the current guidance on physical distancing and all the measures that we recommend in order to protect you, your loved ones and in fact protect all of us."