Mr Drakeford told a press conference in Cardiff that he thinks social distancing will remain “one of the strongest defenses” that we have against the risks that the virus continues to pose.
He also said he had been “very struck” by people in Wales continuing to be careful about keeping their distance from others and moving aside to create space.
“I’m not certain myself that there is a huge thirst for people to give up some of the safeguards that we are all able to contribute in the way that we behave in our lives,” Mr Drakeford said.
He added: “I think they will remain part of the repertoire, here in Wales, during the rest of the summer, maybe into the rest of this year.
“Whether we will be able to move from them being mandatory to just things that we advise people about and ask people to do in their own lives, I think that will depend upon whether we continue to see improvements in the position here in Wales.
“But as part of a personal repertoire of things that every one of us can do to keep ourselves and others safe, I think they will remain part of people’s response to this public health crisis for as long as coronavirus persists.”
His comments came after the he warned that preliminary evidence showed the Indian variant, of which there are 97 cases in Wales, could be leading to greater levels of hospital admissions primarily among young, unvaccinated people.
Outdoor events with up to 10,000 people sitting – or 4,000 people standing – will be able to resume in Wales from Monday while groups of up to 30 people can meet outdoors and extended households can expand to include a third.
But the country’s partial move into alert level one will not include increasing the numbers of people able to meet indoors or attend indoor events due to the Welsh Government wanting more evidence about the effect of the variant.