On Friday, Mr Drakeford confirmed Wales would move to a “stay local” period from Saturday for two weeks before travel rules are lifted in time for the partial return of holiday lets for Easter.
But he said a holiday in Wales would be restricted to those living in the country, as lockdown rules in England mean April 12 is the earliest people living there can go on holiday in the UK.
Mr Drakeford told the PA news agency: “People who let accommodation should not be taking bookings from people who live outside Wales.
“England will still be in a position where their rules say to minimise travel, no holidays, no staying away from home overnight.
“And that means they will not be able to take advantage of accommodation in Wales.
“The Government can only proceed on the basis that the law is going to be observed and it’s for English authorities to enforce the English regulations.
“We will be talking with our local authority colleagues and with the police next week, just to see if there is anything we need to do to mobilise our own enforcement authorities.”
He added: “If the industry were to act irresponsibly, the penalty would be we wouldn’t be able to carry on reopening the industry.
“I know there are rogues in any part of life. But I think that the industry will absolutely recognise that we want to go beyond self-contained accommodation.
“We want the tourism industry in Wales to have a longer and better season this year than we managed last year.
“We won’t be able to do that if people undermine the agreement that we have for how to proceed in that first step.”
People in Wales will only be allowed to stay in holiday accommodation with people from their own household.
Speaking at the Welsh Government’s press briefing in Cardiff later on Friday, Mr Drakeford said he was “making the rules for people in Wales” and said the reopening of self-contained accommodation excluded places where facilities have to be shared with others.
“The basic rules about only going with your own household, that will remain in place, and all the other restrictions we continue to need to observe will be as true if you are in your caravan as it would if you were in your own home,” Mr Drakeford said.
Asked by PA whether there would be any restrictions on people entering Wales from high-prevalence areas when rules across the rest of the UK allow, Mr Drakeford said the Government would “look at what the public health circumstances are at the time”.
“When I’ve talked to the Prime Minister about this in the past, he’s never disagreed with me that it is unadvisable for people to travel from high prevalence areas to low incidence areas.
“Our difference has always simply been about how we enforce that piece of advice.”
He added: “When the day comes when we are able to safely welcome visitors back into Wales from any part of the UK, then we’ll always be very keen to do so.”
Tommy Davies, who runs Coed-Y-Glyn Log Cabins in the village of Glyndyfrdwy, Denbighshire, said Welsh holidaymakers wanting a domestic getaway would make up for the lack of visitors from England until April.
He told PA: “About a week ago or so we started to have a huge influx of booking requests.
“Last year we found we had people from Wales who would normally go to the Lake District and places like that in England still wanted to go on holiday so they booked up local accommodation, so we were just as busy.
“We’re booked up from as soon as we open, and the next availability we have is towards the end of September. And that’s every day across the board. It’s good news.”