The college warned such certificates could potentially give the Government access to sensitive medical data.
It also raised concerns the system could be a limiting factor for hospitality customers who do not have the technology or knowledge to show the certificate.
Martin Marshall, head of the institution, wrote to Mr Gove describing his apprehension over the scheme.
He wrote: “The college is not necessarily opposed to the introduction of some sort of opt-in proof of vaccination document to allow for international travel.
“Our concern about introducing certification for domestic use is that this risks negatively impacting on some patient groups more than others and by doing so widening existing inequalities, including health inequalities, in society.”
He added: “Alternative proof of vaccination must be available for those who don’t have smartphones or are simply less tech-savvy.”
Boris Johnson told MPs he believed pub landlords should be able to to decide whether customers should be asked to present their jab passports.
Labour leader Keir Starmer denounced the Prime Minister’s remarks, saying it would be “wrong” to leave the decision up to pub landlords.
Speaking to the Telegraph, Sir Keir said the implementation such as the documentation in the UK is a complex question.
He said: “My instinct is that, as the vaccine is rolled out, as the number of hospital admissions and deaths go down, there will be a British sense that we don’t actually want to go down this road.”
He added: “I think this is really difficult and I’m not going to pretend there’s a clear black and white, yes-no easy answer on this. It is extremely difficult.
“My instinct is that… (if) we get the virus properly under control, the death rates are near zero, hospital admissions very, very low, that the British instinct in those circumstances will be against vaccine passports.”
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