People forced to self-isolate have expressed frustration at not being included in a programme to help prioritise food deliveries for those unable to leave the house.
Supermarkets have access to a UK government database of 1.5m vulnerable shoppers in England.
Philip Pearce from Bridgend said he was vulnerable and it was "ridiculous" he could not sign up.
The Welsh Government said it was urgently working to resolve the issue.
Mr Pearce said: "I tried to shop at Sainsbury's this morning and because I am classified as vulnerable, I thought I'd be able to register quite easily.
"I went onto the UK government's web page but found I couldn't sign up because I live in Wales.
"It's ridiculous. How am I meant to get my shopping delivered now? I have always had it delivered but now I'm expected to pick it up. This can't be right."
Update: I've written to the chief executive of @sainsburys after constituents told me they've been unable to register for its home delivery service for the over-70s & vulnerable people because the options given to register as vulnerable are for England only. Awaiting a response.— Julie Morgan (@JulieMorganLAB) March 27, 2020
Age Cymru said it was "vital" for people in Wales to be able to sign up.
Its chief executive Victoria Lloyd said: "Many older people have told us that they have to wait for up to three weeks for a delivery while others were simply thrown out of the registration process.
"Systems must be put in place to enable the supermarkets to verify who exactly needs to be given priority in Wales.
"We have contacted the Welsh Government about the issue and we'll be urging the appropriate authorities in Wales to work with the retail sector to make sure vulnerable people are not worried about how they will feed themselves over the coming weeks."
John Evans, who lives in Llanharry, Rhondda Cynon Taff, cares for his disabled wife and has family members who are asthmatic.
He says he also went on the Sainsbury's website to register as vulnerable but it directed him to the UK government page which asked if he was living in England.
"It's ridiculous and frustrating and I'm not the kind of person who isn't familiar with being online," he said.
Retired nurse Beverly Harrison-Wood, 63, from Cardigan, Ceredigion, told BBC Wales the earliest delivery slot she has been offered with any of the major supermarkets was mid-April.
Mrs Harrison-Wood, who has rheumatoid arthritis, lives with her husband, 69, and her 85-year-old mother, said they had about a week's worth of food left.
She said: "There's no chance at all of getting a delivery...
"Unfortunately we can't [sign up for priority] as it's available to England but not to Wales, which is annoying."
She said some small local shops were now doing deliveries: "They are trying their hardest, but we don't shop there and we don't know what they sell."
Sainsbury's has said it is doing its "absolute best" to make online delivery slots available to vulnerable customers.
In an email to shoppers, chief executive Mike Coupe said: "We are also working hard to secure detail for vulnerable people living in Wales, Scotland and Northern Ireland."
The retailer told BBC Wales said it had "proactively contacted 270,000 customers across the UK, including Wales, who had already given us information that meant we could identify them as elderly or vulnerable."
An Asda spokesperson said: "We ask that any customer who has specific circumstance due to coronavirus lets us know in the 'other information' section whilst placing their order."
BBC Wales understands Tesco is examining how it can best make such deliveries to all parts of the UK.
A Welsh Government spokesman said: "We are working with retailers, through the Covid-19 retailers forum and retailer associations, to resolve this issue as a matter of urgency.
"People with certain long-term health conditions are being advised to stay at home and adopt a series of 'shielding' measures for at least 12 weeks.
"They will receive a letter setting out the steps they need to take.
"We will make sure this group of people can get food, medicines and other essentials.
"For those who cannot turn to family, friends and local support networks, we are working closely with the Welsh Local Government Association and the Wales Council for Voluntary Action to ensure support is available locally."