Michael Fabricant said there was no plan to issue "certificates of vaccination" in the UK – or to make the jab mandatory.
However, the Lichfield MP warned that in future some countries may refuse entry to British citizens who are unable to prove they have been vaccinated.
It comes as a petition against Covid passports surged past the 100,000 signature mark, meaning it is set to be debated in Parliament.
Tory MP Mr Fabricant said he had been contacted by "nervous constituents" concerned about having to hold a vaccination passport in order to be allowed into places including supermarkets and leisure centres.
"This is totally untrue and people are getting alarmed over nothing," he said.
“The Government has stated that certificates of vaccination will not be required for use in the United Kingdom for shopping or for any other purposes.
"And while I believe it would be foolish to refuse a Covid vaccination if it is offered, there are also no plans to force anyone to be vaccinated.
"However, as a number of countries abroad have stated that in future they may not allow entry for visitors, except for those holding Covid vaccination certificates, the UK - along with other countries - is investigating how they might be issued.
"This certificate would be similar to Yellow Fever vaccination certificates and others which have been issued in the UK for many years for people planning to visit certain countries overseas."
Mr Fabricant added: "No one will be obliged to obtain Covid vaccination certificates. However, the proposal is that they might be available on request in future for people in the UK planning a visit abroad to countries which might require them.
"If you don’t want to visit that country and be turned away on entry, you won’t need the certificate. It’s as simple and as common sense as that."
Foreign Secretary Dominic Raab has said Ministers were looking at the possibility of bringing in vaccine passports.
He said: "It's something that hasn't been ruled out. It's under consideration. But of course you've got to make it workable."
Labour's candidate for West Midlands Mayor, Birmingham MP Liam Byrne, has said issuing people with Covid passports could allow the West Midlands to "unlock the economy quickly" after lockdown.