Ministers are currently studying the potential use of coronavirus health certificates as England emerges from lockdown.
They could mean people will only be allowed in venues if they have been jabbed, received negative tests or developed antibodies through past infection.
However, Conservative backbenchers, publicans and some scientists have raised concerns about their potential use.
Writing in the Telegraph, Mr Martin said “there is no justification for a passport system”.
The chair of the pub chain said: “For many pubs, hanging on for dear life and devastated by G-force changes of direction, a complex and controversial passport scheme would be the last straw.
“It would inevitably put pub staff in the frontline of a bitter civil liberties war, with some customers unwilling to be vaccinated or unable to have a jab for medical reasons.”
On Sunday, the culture secretary, Oliver Dowden, argued vaccine passports will not be introduced on a “permanent basis” but could be a beneficial tool to restart safely in the short-term.
Mr Dowden, whose brief includes theatres, where certificates could be valuable in relaxing social distancing, had insisted “we need to look at all options” for safely easing restrictions.
“Of course we would never look to do this on a permanent basis, it’s just whether it might be a tool in the short term,” he told The Andrew Marr Show on BBC One.
Welsh First Minister Mark Drakeford said he is prepared to consider their use provided they are “fair and reliable”.
“I think there are definitely prizes to be won through domestic vaccine certification, but there are very big practical and ethical challenges to face as well,” he told Marr.
Professor Mark Woolhouse, a member of the government’s Scientific Pandemic Insights Group on Behaviours (Spi-B), said the use of passports “certainly” had to be considered to make post-lockdown life safe.
“For those activities that it is difficult to make completely safe – I am thinking things like nightclubs, large concerts, mass gatherings – that’s where passports come in, whether it is vaccine passports, test negative passports or even immunity passports,” he told Marr.
However, his Spi-B colleague Professor Stephen Reicher said on Saturday that certificates could compound hesitancy in those already sceptical of vaccines and could therefore be counterproductive by causing lower uptake.
He also warned they could lead to “social division”.
Last week, pub landlords rejected Boris Johnson’s suggestion that it could be up to them to decide whether to screen customers’ certificates on entry.
The prime minister acknowledged the “moral complexities” around a domestic vaccine passport scheme, on which the government will set out more details in early April.
Additional reporting by Press Association