Cabinet Office minister Michael Gove warned that people who refuse a vaccine may be banned from some events in the future.
The government is currently considering the use of vaccine passports for large scale events such as football matches, having already announced they will be required for nightclub entry in England from the end of September.
But Mr Gove warned those who refused to be jabbed may not be able to access such events.
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Speaking to the PA news agency during a visit to the Lighthouse Lab in Glasgow, he said: "Ultimately, if you can be vaccinated and you refuse to, that is a selfish act.
"You're putting other people's health and lives at risk, you should get vaccinated."
When asked if refusal to be jabbed should prevent attendance at some mass events, the minister said: "It depends on which part of the United Kingdom you're in and what the nature of the event is.
"But if you deliberately refuse to get vaccinated and there are certain venues and certain events that require a certain level of safety, then, you know, the terms in which you will be able to get into those venues and those events will be barred to you."
Mr Gove pushed for cooperation across the UK on a Covid-19 certification measure, but stressed it would be for the devolved administrations to make their decisions on the matter.
He said: "I think that the more we collaborate on this, the better.
"The Scottish Government will decide for itself what form of Covid status certification they believe is right.
"We've worked well with the Scottish Government so far, but I think that people would expect there to be, in the same way we've got the same access to NHS services across the United Kingdom, the same access to certification, that would be the ideal, but its for the Scottish Government to decide."
