Andrew Lovett, the chief executive of the Black Country Living Museum, said he believes the vaccine passports to permit a museum visit would be "more of a barrier to that and the opening of the economy, than an acceptable passage to freedoms".
It comes as the UK government is expected to give more details about a proposed ‘Covid-status certification’ – effectively a vaccine passport that could allow people to attend to sporting fixtures, theatres and other public events.
A series of pilot events, including the FA Cup final, cinema screenings and nightclub events are planned to take place up until mid-May.
Mr Lovett said the museum was looking forward to welcoming visitors back through the doors on May 17.
He said that while he has lost family members to coronavirus and has sympathy for those who have suffered during the pandemic – he felt on balance the vaccine passports would be a barrier for the attraction.
Mr Lovett said: "In step three of the Government’s four-phase reopening plan for England, museums can welcome visitors again from May 17, and here at the Black Country Living Museum we are looking forward to that happening.
"I want the museum to provide a safe, equitable visit for everyone, with plenty of fresh air, in a wonderful place that we can all enjoy.
"I have lost close family members to Covid-19 and have enormous sympathy for people that have suffered the pain which this pandemic has wrought.
"However, on balance, I believe that so-called ‘vaccine passports’ to permit a museum visit are more of a barrier to that and the opening up of the economy, than an acceptable passage to freedoms.”
Meanwhile other attractions and theatres across the region say they will await Government guidance on vaccination passports.
Derek Grove, zoo director at Dudley Zoo and Castle, said: "As far as we are aware and from everything we have read and seen, it seems unlikely it will come into force until everyone has been vaccinated, which wouldn’t be until at least the end of July.
"Also, as an outdoor attraction where we can control social distancing as well as having pre-booking procedures in place and full track and trace measures, we are unsure if it would even apply to us.
"But if required, we would of course comply with anything coming into place."
Richard Kay, manager at the Prince of Wales Theatre in Cannock, said: "It has been a long wait to welcome people back to the Prince of Wales Theatre and we look forward to see audiences in our seats and acts on our stage.
"When we can reopen it will be led by the Government guidance at the time which is yet to be confirmed."
A spokesman for West Midland Safari Park in Bewdley added: "Throughout the global pandemic we have adhered to all Government safety guidelines and regularly consulted professional body, BIAZA, for additional safety related advice. We will continue to follow all guidelines and advice as we move through the upcoming months and roadmap out of lockdown.
"We are delighted that Monday’s news provided us with positive confirmation that we will be able to reopen our doors next Monday, April 12, and welcome our guests back to the park."
During a Downing Street press conference on Monday evening the Prime Minister said that the Government would be looking at a "number of signals that you can give that you are not contagious", including having previously had Covid-19, vaccination status and negative test results.
Ministers have ruled out bringing in certification for either the April 12 or May 17 stages of the road map, but the documents could be introduced later this year.
Speaking from Downing Street Mr Johnson suggested that vaccination passports for overseas travel were "going to be a fact of life, probably" because a lot of countries were looking at the possibility.
Shadow health secretary Jonathan Ashworth said Labour was "very sceptical" and wanted more details about how they would work.
He said: "I'm not going to support a policy that, here in my Leicester constituency, if someone wants to go into Next or H&M, they have to produce a vaccination certificate on their phone, on an app.
"I think that's discriminatory."
Senior Tory Mark Harper, chairman of the lockdown-sceptic Covid Recovery Group, warned Covid status certification "will lead to a two-tier Britain".