It comes as the UK reported a record high of new Covid-19 cases, at 88,376, and Ms Sturgeon said Omicron was likely to be the dominant strain in Scotland by Friday.
Pregnant women have also been moved into a higher priority group for Covid-19 vaccines, as chief medical officer Gregor Smith said 98 per cent of pregnant women admitted to intensive care with Covid-19 symptoms have been unvaccinated.
The First Minister has written to Boris Johnson asking for financial backing for further restrictions, adding these “may now be unavoidable”.
It comes as BMA Scotland warned there is a “limit” to how much more NHS staff can cope with, amid staffing shortages, high demand and increased staff exhaustion and burnout.
Members of the public should “do all we are asked to limit spread”, said BMA Scotland chair Lewis Morrison, and not expect any non-urgent issues to be addressed.
Ms Sturgeon told MSPs: “If we don't act now, what we have feared all along, but so far avoided, the overwhelming of the NHS, could happen.”
She added: "This is a really serious situation and we must respond accordingly. I therefore want to strongly underline the advice I gave on Tuesday.
"Please reduce your contact with people from households other than your own as much as you possibly can.
"For now, please stay at home much more than you normally would, and as much as is feasible.
"Right now the risk of getting Covid from interactions with others is high and it is rising.”
Some 5,951 Covid cases were reported in Scotland on Thursday – 45.4 per cent of which were likely to be Omicron.
The Omicron variant is spreading “faster than anything we have experienced so far”, Ms Sturgeon said.
She said: "Omicron has an R number that some assessments estimate to be above four.
"We do not have time to waste on putting in place the protective measures that will help slow this down.
“Lives again are at risk here. Livelihoods are at risk and the NHS is at risk."
Dr Morrison warned the pressure on the NHS caused by Omicron could be “huge”.
“We don't know yet how many hospital admissions, serious illnesses and ITU admissions rising cases will cause,” he said.
"Even if less severe on average, the pressure on the NHS could still be huge. If more routine care is paused again, staff can be redeployed to some extent.
"But after 21 months of the pandemic, and when we came into it so understaffed, there is a limit to how much more of this we can do, and many NHS staff are absolutely exhausted.
"To get through this we must do all we are asked to limit spread. People must access healthcare if unwell, but not expect non-urgent issues to be dealt with just now, and they must be patient and kind to NHS staff.
"When all this is over we must ensure the NHS in Scotland is never again allowed to be understaffed and so vulnerable to surges in clinical demand.”
The Scottish Government has welcomed advice from the Joint Committee on Vaccination and Immunisation (JCVI) to add pregnant women to the “at risk” category of cohort six for Covid-19 vaccination priority.
"Recent data in Scotland shows that almost all (98 per cent) of pregnant women admitted to intensive care units with coronavirus with symptoms were unvaccinated,” said Dr Smith.
“Pregnant women who get coronavirus with symptoms are three times more likely to have a preterm delivery.
“During pregnancy, your immune system is weaker than usual. This means you are more likely to get certain infections and illnesses that can be harmful to you and your baby.
"The best way to protect you and your baby from serious disease and illness is getting the recommended vaccines at the right time. The antibodies you develop after getting a vaccine transfer from you to your unborn baby. This helps give your newborn baby protection.”
The Scottish Government is doing “everything it possibly can” to speed up the booster vaccine rollout, health secretary Humza Yousaf said on Thursday.
Adapted modelling shows around 61,000 jags need to be given each day to achieve the target of delivering 80 per cent of boosters by the end of December, he told the BBC.
The Scottish Conservatives called for mass vaccination centres to be set up with “the urgency that is necessary in light of the new Covid variant”.
Mass centres will be set up at Hampden Park in Glasgow and the Edinburgh International Conference Centre and Corn Exchange in Edinburgh, Ms Sturgeon said, adding the NHS has capacity to reach 70,000 booster vaccines per day.
Those centres are expected to open as early as next week.
Scottish Labour warned the Government not to “choose” between treating Covid-19 and treating cancer.
“Since the start of the pandemic, almost 30,000 of our fellow Scots have died from cancer,” party leader Anas Sarwar said.
Mr Sarwar highlighted figures from Public Health Scotland showing that almost one in five of the most urgent cancer cases are not starting treatment on time.
“We can’t have an NHS that chooses between treating a virus or treating cancer,” he said.
“That means there must be no pause to screening programmes, genuine acceleration so we can catch up, and no cancelled cancer operations.”