People in Wales will be able to prove they have had a vaccine via a website "within days".
People in England can get a digital version showing their vaccination status via their NHS Covid Pass on the NHS app.
First Minister Mark Drakeford said that a similar service will be available in Wales "within days" however it won't be via app and will not be available in Welsh for "several months".
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Caerphilly MS Hefin David asked the First Minister about plans for the app being rolled out in Wales. Mr Drakeford had previously said it would take four weeks to arrive in Wales in comparison to England.
Mr David used the story of a constituent who needs to prove she has had her jabs to attend an event.
Her health board told her she can receive a certificate through the post, but the woman described that as being "archaic and slow".
Mr Drakeford said that due to" technical reasons", largely connected to the reconfiguration of the English solution to meet Welsh requirements, it wasn't possible to launch the app in Wales at the same time in Wales as it was in England.
He said: "I don't agree that the solution that has been in place in the last four weeks is archaic. Over 10,000 people have received certificates through that way of doing things and it's due to the very hard work of the team in the Swansea Bay health board that's possible.
"Once the English system manages to do its job and make access for Welsh people available to it but I'm afraid it won't be available in Welsh despite repeated requests to the UK Government to respect the law here in Wales, they tell us they won't be able to do that for several more months. But we do anticipate in the next few days it will be possible for Welsh citizens to use the same solution, albeit not via the app but via a website portal. The journey thereafter will be identical to the app and Welsh people will be able to use it in real time in the way that the English system has been available in England since the 17th of May."
The Department of Health has been contacted.
