Mark Drakeford spoke out as Paris goes into a month-long Covid-19 lockdown over fears of a third wave of the virus spreading across France.
In Wales over the last week there have been two localised flare-ups in Merthyr and Anglesey which the First Minister attributed to people not sticking to the rules over household mixing and social distancing.
Mr Drakeford told the Welsh Government briefing he was “concerned” to see reports of a third wave of coronavirus hitting France.
“I’ve never come to this podium and said to people in Wales that coronavirus is all over and that it will be completely behind us during this calendar year,” he said.
“I hope it will be and I absolutely hope it will be, but I don’t think it’s responsible to say to people that is a guarantee that anybody could offer them.
“As things are improving and our aim of course will be for things to go on improving, for us to be able to do more to restore freedoms to people over the weeks and months ahead.
“But coronavirus has been full of unpleasant surprises.
“Just as we have seen in Paris over the last few days, France was doing incredibly well only a few weeks ago and are now finding a sudden and significant flare-up.
“Nobody should think that we are immune from that, nobody should think we can drop our guard and plan on the basis that coronavirus has gone away.
“That will not be the approach taken by the Welsh Government.”
Meanwhile, there have been a further 201 cases of coronavirus in Wales, taking the total number of confirmed cases to 207,438.
Public Health Wales reported nine further deaths, taking the total in the country since the start of the pandemic to 5,476.
Just over 1.2 million people had received a first dose of the vaccine and nearly 320,000 second doses had been administered in Wales – one in 10 of the population.
Mr Drakeford said Wales had “flexible plans” to deal with a delay in vaccine supplies to the UK from India.
“We are confident that no appointments for second doses will be cancelled and all appointments for the rest of this month will be honoured,” he said.
“We’ll then adjust our plans to make sure that we continue to invite as many people as possible for vaccination.”
He said the overall public health situation remained “stable” at about 44 cases per 100,000 people and a positivity rate of 3.9%.
“We are particularly concerned about an apparent reluctance in some places to engage with contact-tracing teams,” he said.
And he also urged people to watch a potential Wales rugby Six Nations grand slam at home within their household.
“If you’re watching Wales this weekend, please watch with members of your household only,” he said.
“The last thing we want is to mark a potential Grand Slam weekend with a surge in Covid cases.”