Some 51 per cent of Covid cases in Scotland are now estimated to be the Omicron variant, the First Minister told a Covid-19 media briefing on Friday.
It comes as new research suggests the variant can “very substantially” evade immunity from previous infection or two vaccine doses, posing a “major, imminent threat to public health”.
Cases in Scotland have increased by more than 40 per cent in the past week, Ms Sturgeon said, warning that this should be expected to accelerate even further.
"The tsunami I warned about a week ago is now starting to hit us,” she said.
Ms Sturgeon urged people to stay at home in the run-up to Christmas, saying the emergence of Omicron has been the “cruellest of blows”.
The First Minister warned of a “massive number of patients” needing hospital care in the coming period.
She said: "Even if [Omicron] did turn out to be generally a little less severe for most people - and let me stress we still don’t know that to be true - for some people it will still cause serious illness and hospitalisation. Tragically, more people will die.
"And even if the number of people falling seriously ill is a smaller percentage of cases than with Delta, the basic fact of arithmetic is inescapable - a smaller percentage of a much bigger number of infections will result in a massive number of cases needing hospital care."
A study from Imperial College London has found no evidence of Omicron having lower severity than Delta, but researchers said data on hospital admission was very low at the time of the study.
The study also found that the risk of reinfection with Omicron is 5.4 times greater than that of the Delta variant.
Imperial College London’s Professor Neil Ferguson said: “This study provides further evidence of the very substantial extent to which Omicron can evade prior immunity, given by both infection or vaccination.
“This level of immune evasion means that Omicron poses a major, imminent threat to public health.”
New rules came into force for Scottish businesses on Friday, requiring them to take “reasonable measures” to reduce Covid transmission.
This includes managing queues and crowding, as well as enforcing the wearing of masks.
The hospitality sector has been encouraged to return to table service where practical, and businesses have also been asked to consider a ticketing system during peak festive opening hours where appropriate.
Latest Office for National Statistics figures estimate one in 80 people in Scotland had Covid-19 in the week to December 11, unchanged on the previous week and below September’s peak of one in 45.
In Wales the figure is around one in 55 people, while it is one in 50 in Northern Ireland.
Commenting on the First Minister’s update, Scottish Labour’s Health and Covid Recovery spokesperson Jackie Baillie said: “There is no doubting the level of concern this variant is causing across the board.
“It has reached every part of Scotland, and is moving exponentially – there is clearly no room for complacency.
“If it does spread at this rate, staff absences alone will wreak havoc with essential services.
“We all have a role to play – by getting our boosters, taking lateral flow tests, and using our judgement.
“Thousands of businesses are already feeling the effects of this advice, and we need to make sure they get the support they need.
“The Scottish and the UK governments need to put politics aside and work together to save lives and livelihoods.”