John Spellar said it would be a "straightforward process" to issue people with a plastic card or mobile app proving they had received the jab, which could then be presented at venues.
He said it would help save the country from the "human and economic disaster" of thousands of venues and attractions being forced to close down for good due to the pandemic.
Boris Johnson had previously ruled out the idea but has now called a review into the prospect of introducing a vaccine certificate of proof.
Ministers have said it seems highly likely that some form of proof of vaccination will be required for international travel to some countries.
Mr Spellar, the Labour MP for Warley, said: "Why not have a vaccine passport? Huge advances in technology over the past decades mean that it should be a relatively straightforward process.
"The NHS keeps records of everyone who has had the jab – I have my own card here – and this information could be stored on a plastic card produced in a secure environment or possibly on a mobile phone app, and carried around in a pocket ready to be presented on entry at any commercial venue.
"Let us be clear that the NHS already issues yellow fever cards as the proof of vaccination that some countries require before people can visit."
Michael Fabricant, the Conservative MP for Lichfield, said there was no need for vaccine passports to be introduced for UK use.
"I do not believe there is going to be the need for any certification for use in the UK," he said.
"The scientists reckon that once 80 per cent or so of the population have been vaccinated, while Covid won't be completely eliminated, it will be so rare it will not be a major factor requiring people to get vaccinated.
"For example, although there is some flu in the summer, in practice it is irrelevant whether people have been vaccinated against it or not, because hardly anyone has become infected with it to pass on to others."
Mr Johnson said on Monday that all Covid restrictions could end by June 21 providing strict conditions are met.
On the review of vaccine passports, the PM said: "In this country we've never thought in terms of having something that you have to show to go to the pub or the theatre.
"It's a deep and complex issue that we need to explore."
Reports suggest a new app for travellers is due to be rolled out within weeks, with the digital pass allowing border agencies to verify that air passengers have received their Covid jabs by approved authorities.
The move is seen by some as key in aiding the widespread resumption of foreign travel, and could replace current travel restrictions such as triple testing of passengers, quarantine hotels, and ten-day mandatory quarantine.
A petition against vaccine passports has reached more than 170,000 signatures and will be discussed in Parliament.