Ms Jewell said 370,000 unpaid carers will miss out on the money despite providing care worth an estimated £8.1bn to the Welsh economy.
She said: “Unpaid carers in Wales and those not on the care register must be given parity of recognition because the care they provide is just as selfless, and just as invaluable, as that provided by paid carers and those on the register.
“Scotland is taking steps to provide that parity of recognition – that should be mirrored here in Wales.”
She also said care home staff such as cooks and cleaners should get the £500 and that levels of care home staff pay need to be looked at in the longer-term.
Ms Jewell added: “This pandemic has forced us to look at which jobs in our society are essential, and those who look after and support the most vulnerable in our society deserve to be recognised for the incredible contributions they make.”
A Welsh Government spokesperson said: “Although unpaid carers are not eligible for the £500 payment, we are working closely with carers and their representatives to ensure they get the support and recognition they deserve.
“We have established a new £24m Third Sector Covid-19 Response Fund, which includes services supporting unpaid carers. We have also allocated £40m of extra funding to local authorities for extra costs incurred in adult services due to the Covid-19 pandemic.”
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