Vaughan Gething said he was "looking again at charging arrangements" for people from countries without reciprocal arrangements with the UK.
In a new BBC Wales poll, 79% of those surveyed said they would increase charges for visitors from outside the UK for using the health service.
But Mr Gething said such charges were a "marginal area" of NHS activity.
Speaking to The Wales Report on Wednesday, he said: "We have reciprocal arrangements with most European countries, and as long as those reciprocal arrangements work I see no reason to intervene and change those.
"However for people outside the UK and Europe where we don't have those, we're looking again at charging arrangements."
"Later in the year I'll get to make a decision on what charging may or may not look like."
But the health secretary added: "This is such a marginal area of activity."
"Really, when you're talking about the central funding of the health service, with the big challenge that we face, the actual conversation about charging people from abroad is an absolute distraction."
Asked whether he would consider charging patients who have illnesses caused by their lifestyle choices, Mr Gething said: "If you're really saying, for example, that someone with lung cancer who smoked should therefore be charged for their treatment.
"I actually think that when you get into real examples like that, people will very quickly say that isn't what I think should happen.
"When you think about the practical reality of it, it isn't that simple at all."
Mr Gething warned while the Welsh Government had made "significant additional commitments" to the health service from its budget, there would be difficult consequences if austerity continues across the UK.
"The challenge will be if we don't see the tide turned back on austerity every single part of the UK health service system will face really awful choices, that I don't think the public will tolerate."
The Welsh Government is reviewing NHS charges for visitors from outside the UK, the health secretary has said.