The Cabinet Office minister warned the “finely balanced” benefits had to be set against any “hassle factor” of implementing them.
Mr Gove has been leading a review into the use of Covid status certification for the Government, visiting Israel as part of the process to assess the effectiveness of a similar “green pass” scheme deployed in the Middle East country.
He told the Public Administration and Constitutional Affairs Committee that if a similar scheme was introduced in Britain it was always intended for a time-limited period.
Asking people to prove their Covid status could allow large events, such as football matches, to resume at full capacity if coronavirus restrictions look likely to remain in place.
Mr Gove’s review into the potential use of Covid status certification – which would include not only vaccine details but also whether someone has a negative test result – had been due to report this month, but that has now been delayed until after the Commons returns from a recess in the week of June 7.
The Chancellor of the Duchy of Lancaster said if such a scheme proved too costly or too much “hassle” for the hospitality industry, then the Government would not pursue it.
The NHS app has already been altered to allow users to prove their vaccine status and Mr Gove said further changes were in the pipeline so test results could be declared as well.
Asked by MPs how balanced in his view were the costs and benefits of Covid status certification, he replied: “Finely balanced.”
The Chancellor of the Duchy of Lancaster said there were “some significant outstanding factors” to consider but it could help “economic and social life… return more quickly”.
He said the possible introduction of the passports was not necessarily linked to the next stage of the road map on June 21 at the earliest.
Mr Gove said: “We have been looking at every stage the impact certification might or might not have on the economy.
“So, to take a case in point, if it is the case that we want to see the restoration of Premier League football, which I certainly do, then in order for that to happen we would want to have, and indeed Premier League teams would also want to have, their stadia full to maximum capacity.
“Certification may play a role in that if the alternative were to, for example, to continue with social distancing and other forms of restrictions such as crowd capacity limits.
“So, in that sense, and that is just one example, the deployment of certification and the investment in that infrastructure would enable the economic and social life of the country to return more quickly and safely.”
Mr Gove said there were “frictional costs” involved with certification as testing would have to be continued for those who had not been vaccinated.
Mr Gove denied that vaccine passports were a way of encouraging take-up of jabs and said many venues would be excluded from such measures.
The Cabinet minister said public transport operators, libraries, Government buildings, job centres and essential retail would not be allowed to ask for someone’s Covid status before entry, should the scheme be brought in.
Dr Susan Hopkins, interim chief medical adviser for NHS Test and Trace, said data indicated that opening up events to vaccinated people or those who could prove they had either previously contracted Covid or were negative could reduce the transmission risk by as much as half.
It comes after Culture Secretary Oliver Dowden heralded pilot events a “real success” after only 15 positive cases were detected among the 58,000 participants, who attended events ranging from an FA Cup semi-final at Wembley to a nightclub in Liverpool.