Nicola Sturgeon said the level means the ‘likelihood of getting it just now if you mix with others is high’.
Daily coronavirus cases have hit a record high for the second consecutive day at 16,857.
Figures published by the Scottish Government on Thursday show 71,612 new tests for Covid-19 reported results and 27.1% were positive.
First Minister Nicola Sturgeon said the record reflects the Omicron variant of the virus being “very, very infectious” and added the “likelihood of getting it just now if you mix with others is high”.
The new daily case figure breaks the previous high of 15,849 announced on Wednesday.
The latest data shows nine deaths from the virus were recorded north of the border in the previous 24 hours.
This takes the Covid-19 death toll in Scotland under the daily measure, of people who first tested positive for the virus within the previous 28 days, to 9,845.
Ms Sturgeon also addressed the rise in numbers of people in hospital with the virus, which jumped by 131 to 810 in 24 hours.
Of these patients, 34 were in intensive care, down two.
She posted on Twitter: “Yet another record tally of reported cases in today – reflecting fact that Omicron is very, very infectious.
“Likelihood of getting it just now if you mix with others is high. Tho remember – being boosted gives you significant protection against becoming v ill with it.
“Just as notable than cases is the steep rise in hospital occupancy, the largest single day increase in a while – a reminder that even if there is a lower % hospitalised through Omicron, sheer volume will still put acute pressure on NHS – and result in serious illness for many.
“Concerning those these numbers are, they would be even higher but for good compliance with public health advice.
“As we approach the New Year, I am appealing to everyone to keep following this advice – for you own sake and also to help the NHS.”
She urged people to continue to limit contact with people in other households and to take a test before heading out if mixing with others.
Ms Sturgeon also reminded people who test positive to isolate, everyone to wear face coverings in indoor places, maintain hand hygiene and get their booster vaccination in a drive to have people protected by the new year.
The figures published on Thursday show a total of 4,381,226 people have received their first dose of a Covid-19 vaccination, 4,012,490 have received a second dose, and 2,944,977 have received a third dose or booster.