From 6pm on Friday, Wales’s pubs, cafes and restaurants will have to stop serving alcohol on their premises, as part of a clampdown in coronavirus restrictions.
But while he admitted that the law does not prevent people from making such a journey, he stressed that the Welsh government’s “clear unambiguous advice to people, is not to do it”.
“Because to do it is to add to the risks that we are already facing and those risks are already driving coronavirus rates rapidly upwards in Wales,” Mr Drakeford told a press briefing on Friday.
“So, please, don’t do it. It is not good for you. It is not good for anybody you know, it is not good for the rest of the population of Wales.”
He concluded: “So, that’s the position. Legally, it’s not preventable but in every other way, it’s not to be advised.”
His comments came as the latest weekly Covid-19 figures painted a bleak picture for Wales.
Almost two thirds of all local authority areas in Wales have a seven-day rate of at least 150 cases per 100,000 people, Mr Drakeford said, with rates continuing to rise in all but two areas.
In Neath Port Talbot and Blaenau Gwent, this exceeded 400 cases per 100,000 people.
In light of the “very serious" situation across the country, Mr Drakeford defended his government’s alcohol ban as the “right thing” to do.
“I take the decisions that I do because I know that they are the right decisions and that they will save lives here in Wales,” Mr Drakeford told the same press briefing.
“Even when the decisions are difficult, so long as I can look at myself in the mirror and know that I am doing what I believe – with all the evidence that we draw on and the advice that we get – that I am doing and this government is doing the right thing.
“That is what has to matter to me, not whether it is in a temporary way unpopular or that other people might take a different view.”
Mr Drakeford warned the country’s restrictions on hospitality were not likely to be lifted when they are reviewed on December 17.
His warnings came as JD Wetherspoon confirmed plans to keep eight of its pubs open in Wales from Saturday.
The move follows a meeting between Wetherspoon chairman Tim Martin and members of the Welsh Parliament who are opposed to pub closures.
Wetherspoon said pubs will effectively trade as cafes in Cardiff, Newport, Caernarfon, Cwmbran, Mold and Wrexham.
Tim Martin said: “I met with Conservative leader of the opposition Paul Davies MS and Conservative chief whip Darren Millar MS at our pub, The Mount Stuart, in Cardiff earlier this week.
“They are opposed to the Welsh pub closures and were keen for Wetherspoon to keep some of the company’s pubs open.
“As a result we have decided to keep eight of the pubs open from 8am to 6pm throughout the week.”