Teachers and other education staff – who are also offered the chance to test regularly to prevent them from passing the virus on to their pupils – are also not taking the tests.
Public heath experts have warned action needs to be taken to encourage more pupils and teachers to engage with the scheme.
New figures obtained by the Daily Telegraph newspaper from Public Health Scotland data show that in the week to May 30, fewer than one in every 20 pupils in S3 to S6 took part in the programme, with an uptake rate of just 4.9 per cent.
For younger secondary pupils, uptake was just 6.3 per cent.
More than two thirds of school workers, including teachers, also did not take part in the testing scheme.
The data shows that since the scheme was set up, 70 per cent of S4 to S6 pupils have never taken a single test. Eight in ten younger secondary pupils have also not taken part since testing was expanded in late April.
Linda Bauld, professor of public health at the University of Edinburgh, said that "incentives" could be introduced to persuade young people to take part in the scheme.
"Regular asymptomatic testing is particularly useful in settings like schools where infections affect not just the person testing positive, but also others who have to self-isolate, disrupting education and work," she said.
"To improve uptake, clear and consistent messaging is needed, robust systems for recording, and even some form of incentives, appropriate to the setting and age group could be considered."
In Moray, where an earlier spike now appears to have been brought back under control, almost half of teachers took part in the week to May 30, along with 18.6 per cent of younger secondary pupils and 12.4 per cent of older pupils – the highest rates in Scotland.
Oliver Mundell, education spokesman for the Scottish Tories, said the figures were "concerning".
He said: "The example of Moray shows what is possible. Their rapid reaction to Covid outbreaks has got the virus under control."