The first people in the UK are in hospital with Omicron infections, Nadhim Zahawi has said.
The new variant of coronavirus now accounts for a third of cases in London, the education secretary said.
With two doses of a vaccine "not enough" Mr Zahawi encouraged people to get a booster jab - those aged 30 and over are eligible to do so from Monday.
As of Saturday, there have been 1,898 confirmed cases of the Omicron variant in the UK.
But the true number is likely to be far higher.
Scientists from the London School of Hygiene and Tropical Medicine (LSHTM) have warned that the UK will face a substantial wave of Omicron infections without further restrictions beyond the Plan B measures announced last week.
These include recommending people work from home if they can, expanding mask-wearing rules and introducing Covid passes for entry to some venues - with parliament to vote on the changes on Tuesday.
Mr Zahawi told BBC One's Andrew Marr Show the new variant was a "big bump in the road" on the journey from pandemic to epidemic.
He said a "national endeavour" was needed on the vaccine roll-out with the country in a "race against Omicron".
The current measures in response to the variant were "proportionate", the education secretary added.
Asked by Andrew Marr if he could guarantee all schools would be open in January, Mr Zahawi said he would do "everything in my power" to ensure all of them stayed open and protected but he stopped short of giving a guarantee.
Dr Susan Hopkins, chief medical adviser for the UK Health Security Agency, said that she expected to see an increase in the number of people in hospital with Omicron infection.
It is not clear if those people who are in hospital with Omicron are there because of the virus or for other reasons.
She said there had not been a report of a death from the variant in the UK yet, although she pointed out that it had only been identified two weeks ago. It is two weeks after infection that you would expect to see people admitted to hospital, with deaths coming after that.
It is "inevitable" that there was going to be a big wave of infections but what was not clear was the impact that would have on hospitals, she said.
She said the sheer weight of numbers of people being infected with Omicron means it will find the unvaccinated or people who have had a poor immune response to the vaccine.
"This is a big wave coming straight at us - if we see even half the severity that we saw with Delta then we are facing a very large number of hospitalisations and potential deaths," she said.
Mr Zahawi said that even if Omicron was less severe than other variants, due its infectiousness, "a small percentage of a very large population will put many people in hospital".
Although she described the current measures as "sensible", Dr Hopkins said more measures may be needed and said the government had "very difficult" decisions ahead.
Chris Hopson, chief executive of NHS Providers - the association of NHS trusts - described staff as "completely flat out and beyond full stretch" with it already being "busier than before at this time of year", even before the peak of the Omicron variant.
The booster roll-out has been expanded in response to the new variant and from Monday people 30 and over will be able to book their top up shots.
The time people have to wait between second and third vaccine doses has also been reduced to three months - rather than after six months.
Labour leader Sir Keir Starmer said he was "very concerned about the new variant" and confirmed that his party would back the government's measures to slow the spread of Omicron.
But he accused the government of a "failure to plan" and being "behind the curve" with the booster programme.
BDST: 1855 HRS, DEC 12, 2021