The Welsh leader said that only people carrying out 'essential' work would be allowed in and out of the principality from Thursday, after the Prime Minister's shock weekend announcement.
Mr Drakeford has said the border between England and Wales may well now be the hardest it has been 'for several centuries at least'.
The effective bar on Welsh people travelling into England came as he revealed a new set of national rules would be introduced across Wales once its own 17-day firebreak lockdown ends on November 9.
And he took a swipe at English people seeking to visit Wales after that date to escape the lockdown.
'We will be coming out of our firebreak just as England begins a month-long lockdown and it is really important that as we open up, Wales doesn't become an escape for people seeking to circumvent the new tighter restrictions imposed by the Prime Minister,' he said.
Mr Drakeford told a press conference that England and Wales share a 'long and porous border', with around 150,000 people crossing daily when lockdown is not in place.
'People who live in Wales but work in England will have a reasonable reason for travelling to work, and people who live in England and work in Wales clearly have a reasonable excuse for coming across the border to work here,' he added.
'But it will be a restricted list of essential purposes, rather than the normal to-ing and fro-ing across the border that you would have seen in less fraught and difficult times.'
The Welsh leader said that only people carrying out 'essential' work would be allowed in and out of the principality from Thursday, after the Prime Minister's shock weekend announcement
The effective bar on Welsh people travelling into England came as he revealed a new set of national rules would be introduced across Wales once its own 17-day firebreak lockdown ends on November 9
Nicola Sturgeon says she may bring in a new full lockdown in Scotland as long as Chancellor Rishi Sunak will pay for it
Scotland's First Minister has said she will consider whether to impose another national lockdown now the furlough scheme has been extended.
Nicola Sturgeon said she hopes to hear from the Treasury on whether the furlough scheme extension will only be available during England's lockdown or if it can apply in other areas, such as Scotland, if they go into lockdown later.
Speaking at the Scottish Government's coronavirus briefing on Monday as the new five-level Covid-19 restriction system came into force, she said she would ideally take time to assess the impact of this before any lockdown decision.
But she said she requires 'absolute clarity' on furlough before deciding.
The First Minister said she and her counterparts from Wales and Northern Ireland pressed at a Cobra meeting earlier on Monday for the furlough scheme to be available for the devolved administrations whenever they require.
She added she hopes to 'get absolute clarity on that point from the Treasury today'.
Ms Sturgeon said: 'I made clear last week, when I set out the levels that would apply initially, that we might yet have to go further and that we can't rule out - and shouldn't rule out - a move to Level 4 for all or parts of the country.
'And while that decision would never be easy, there is no doubt that the availability of a more extensive furlough scheme of the kind that the Prime Minister announced on Saturday would make it slightly less difficult because workers would have more of their wages paid.'
The Prime Minister's official spokesman said: 'The furlough scheme is UK-wide and all changes to the scheme apply UK-wide, and they have done throughout the crisis.'
It is not yet clear how the ban would be policed.
Mr Drakeford made a similar move last month after the start of the Welsh firebreak. Police commissioners in Wales suggested they could set up road blocks and follow up tips from the public.
However, they have admitted there was not the capacity to 'line the border with patrol cars'.
Mr Drakeford said the Welsh Government decided to impose the firebreak lockdown when Wales was 'tracking a reasonable worst-case scenario' rather than exceeding it.
Some of the new measures to be introduced from November 9 are still being finalised.
But they include:The need to maintain two-metre social distancing and wear face masks in enclosed public places, including on public transport and taxis, will continue;The requirement to work from home whenever possible will remain;People should only meet with their 'bubble' in their own home and only two households will be able to form a 'bubble'. If one person from either household develops symptoms, everyone should immediately self-isolate;Up to 15 people can take part in an organised indoor activity and up to 30 in an organised activity outdoors, providing all social distancing, hand hygiene and other Covid-19 safety measures are followed;All premises, such as restaurants, cafes, pubs and gyms, closed during the firebreak will be able to reopen. Following the announcement about the English lockdown, ministers are having ongoing discussions with the hospitality sector about the detailed rules for reopening. This includes about meeting in public indoor spaces;As part of keeping risks to a minimum, people should avoid non-essential travel as much as possible. There will be no legal restrictions on travel within Wales for residents, but international travel should be for essential reasons only.
Mr Drakeford said that in addition, all schools will reopen, churches and places of worship will be able to resume services, local authority services will resume and community centres will be available for small groups to meet safely indoors.
He said: 'Each of us has an important part to play in slowing the spread of coronavirus in Wales and saving lives - we cannot do this without your help.
'Everyone has made so many sacrifices this year already. To make sure we do not lose all this hard work, we need to carry on looking after each other and keeping ourselves safe.
'This is a virus which thrives on human contact.
'Social contact is important to all of us but to keep ourselves and our loved ones safe, we need to think carefully about all our meetings and contacts with other people and try and reduce them to reduce our risk of infection.
'Rather than us asking what we can or can't do, we need to ask ourselves what should we be doing to keep our families safe.
'Government rules and regulations are here to help. But the real strength we have is in the choices we make and the actions we take together.'