The First Minister called for a “mature, grown-up debate” about the idea in a Covid-19 media briefing on Tuesday.
She said she is “open-minded” about the idea, but warned that practical and ethical questions remain.
“I think we will see some kind of vaccine certification starting to be used,” she said, but added: “We have some issues to think through in order to give assurance to the public.”
"I’m not one of these people that says never, ever, ever, because I think we need to be open-minded to anything that helps us get back to normality,” she said.
“But nor am I one of these people that just says we’ll just forget some of the really complex issues that we’ve got to think through.
“Let’s have a grown-up debate about this and trial where that is appropriate, learn lessons as we go, but get to the right position through a mature, grown-up debate.”
National Clinical Director Jason Leitch said he also expects to see a form of “Covid certification” in use, but warned that the concept of “vaccine passports” may be misleading.
“I think Covid certification in the round will become a thing,” he said.
"TV companies are already using Covid certification to allow them to film, so that already exists. That may be about tests, that may be about a previous infection, and it may in future be about vaccination.
"International travel at some point is already doing that – some airlines are insisting on it, some countries are insisting on it [...] that won’t be up to us, we will have to take a view on what a certificate looks like for the Scots.”
He added: “Other than that I think you get into very difficult territory, and it will be a judgement for politicians all over the world what that certificate means for entertainment, for sport, for other areas.”
Scotland’s Health Secretary, Jeane Freeman, said on Monday the Government was working to develop the tools needed for digital vaccine certificates.
Ms Freeman said she favours digital certificates over paper versions as she believes the latter would place an unnecessary burden on the health service.