Covid rules in Wales will be reviewed weekly, instead of every three weeks, following the discovery of the Omicron variant.
But Wales won't see any major changes to its Covid regulations today (10 December) as the decision has been made to keep the Alert Level at 0.
The First Minister discussed the findings of the Government's latest three-week Covid review in a press conference today, with people being urged to get their booster jabs.
Mr Drakeford warned Omicron cases are likely to rise quickly in Wales as the variant spreads in the community.
He said: "The numbers in Wales are low at the moment. But we must be prepared for these to rise quickly and steeply over the coming days and weeks, as it takes root in our communities.
"There is still a lot we don’t know about omicron – the world’s best scientists are working around the clock to understand more about it. But we do know that this is a very fast-moving form of the virus."
Getting a third dose of the vaccine is the best protection against the new variant, the First Minister said.
He added: "Every single vaccination is a small victory against the virus - so please make getting your vaccine or booster a priority."
Meanwhile, people are being asked to continue wearing face coverings in all public places and take regular lateral flow tests before going out, to try and protect others in the lead-up to Christmas.
'We are not back at square one'
Those who test positive must self-isolate and arrange for a PCR test.
Mr Drakeford said: "The emergence of the Omicron variant is another worrying development in this long-running pandemic. We are concerned about the speed it is moving and its potential to infect large numbers of people.
"We are speeding up the rollout of boosters in response to the new variant. We're increasing the number of clinics and extending opening hours."
But he added: "We are not back at square one."
"Please do everything you can to protect yourself and your loved ones. Please follow all the advice and all the measures which have kept us safe over the last couple of years. And let's stay safe and well this Christmas."
The Welsh Government say more than a million people have already received their booster vaccine. At the moment there are nine confirmed Omicron cases in Wales.
Ministers have said preparations must be made for cases to rise quickly and sharply, given there is now widespread community transmission in England and Scotland.
Russell George, the Welsh Conservative Shadow Health Minister, has welcomed the Welsh Government's announcement.
“I am pleased no major restrictions will be introduced today by the First Minister.
“We understand that there is more to learn about Omicron, but it’s important that we get evidence to justify restrictions rather than use the absence of evidence to make decisions, like with vaccine passports.
“We know vaccinations are the key to a society living with coronavirus, so it’s vital Labour ministers now use this period to ramp up the booster programme to protect lives and ensure we keep our hard-earned success.”