Scotland's First Minister said a rise in cases is "virtually certain" and warned it would "run riot" through the population, with modelling in a Scottish Government evidence paper showing infections could surge to as many as 25,000 a day in the worst case scenario.
Ms Sturgeon announced stricter isolation rules in response to the modelling during a coronavirus briefing in Edinburgh, confirming that from Saturday household contacts will be asked to self-isolate for 10 days regardless of their vaccination status or a negative PCR test.
The rate at which cases of the new variant double is between two and three days, the paper said, and it is highly probable that Omicron will become the dominant variant within Scotland "very quickly".
The upper range of the document's worst-case scenario projection for the Omicron variant falls just short of 25,000 cases a day by December 20, while the most-likely range of the worst-case scenario will see cases hit a little over 15,000.
In the best-case scenario, cases will peak at just over 1,250.
More than 1,000 confirmed, probable and possible Omicron cases have been reported in Scotland so far. A new Scottish Government paper says there are expected - though not confirmed - cases in the Scottish Borders.
The First Minister said 5,018 positive cases of coronavirus were reported in the past 24 hours, adding: "This is one day's figures, but as you can see it is a sharp rise on the average of around 2,800 per day that we have been reporting recently.
"It underlines our fear that a new wave may indeed be starting."
She said Omicron is likely to become the dominant variant of Covid-19 in Scotland in "days, not weeks".
Ms Sturgeon added: "Omicron right now is rising exponentially, indeed what we are seeing in the data just now is perhaps the fastest exponential growth that we have seen in this pandemic so far.
"If that continues, and we have no reason at this stage to believe that it won't, Omicron is going to very quickly overtake Delta as the dominant strain in Scotland.
Even if the Omicron variant cases less severe illness than other strains, a "massive number" of patients may still need hospital care, Ms Sturgeon said.
She said "a smaller percentage of a bigger number will still result in a massive number of cases who might need hospital care".
She added: "Given the volume of people who could be infected by Omicron because of its greater transmissibility, even if most of those cases are mild, the number of cases of serious illness will put massive strain on the ability of the NHS to cope."
A "significant strain" will also be put on the economy given the number of people who would be required to self-isolate as a result of the transmissibility of the new variant, the First Minister said.
She also stressed that although evidence suggests Omicron can evade some immunity conferred by vaccines, people should still get jabbed.
Ms Sturgeon will take part in a Cobra meeting chaired by UK Government minister Michael Gove with the first ministers of the other devolved nations on Friday afternoon to discuss Covid-19 data and co-ordination on the response.
Listen to our podcast on Covid-19