His comments came after the Government’s vaccine tsar Nadhim Zahawi suggested hospitality and other businesses could bar those who have not had a Covid-19 vaccine.
Asking about an 'immunity passport' on BBC Breakfast, Mr Gove said: "Let’s not get ahead of ourselves, that’s not the plan.
"What we want to do is to make sure that we can get vaccines effectively rolled out."
He added: "Of course, individual businesses have the capacity to make decisions about who they will admit and why.
"But the most important thing that we should be doing at this stage is concentrating on making sure the vaccine is rolled out."
On Monday, Mr Zahawi, the minister responsible for the rollout of a vaccine, said it would not be compulsory to receive and injection but pubs and restaurants could demand to know if a customer has received a coronavirus jab before permitting entry.
Asked whether people who get the Covid-19 jab will receive some kind of “immunity passport” to show they have been vaccinated, he told the BBC: "We are looking at the technology.
"I think you’ll probably find that restaurants and bars and cinemas and other venues, sports venues, will probably also use that system – as they have done with the (test and trace) app."
Such a regime could result in people without the vaccine facing severe restrictions.
Mr Zahawi said: "I think people have to make a decision.
"But I think you’ll probably find many service providers will want to engage with this in the way they did with the app."