Councils in England are being allowed to raise the tax by 6% over two years to plug a care funding gap.
But Wales' Social Services Minister Rebecca Evans told BBC Wales that increasing the tax was not "fair" and "not an approach we're taking".
The Welsh Local Government Association has warned councils face a Â£92m social care "black hole" in 2017-18.
Leading experts say the cost of providing care could double to Â£2.3bn by 2030.
Speaking on The Wales Report on Wednesday, Ms Evans said: "Some parts of Wales have a much larger proportion of older people than others.
"And obviously if we were to put the burden on local authorities to raise council tax to pay for that, it would disproportionately affect some parts of Wales more than others."
Ms Evans said Welsh ministers wanted to take a longer term approach towards social care but "we do need the UK government to help us with this".
"We don't know what our long-term funding is going to be from the UK government," she said.
"So these are issues that are beyond our control, but within our control we're certainly doing everything we can to make social care good quality and fair across Wales in terms of paying for care as well."
"I'm under no illusion how fragile the sector is in Wales, and the fact that Welsh Government does need to support it," she added.
Mario Kreft, chair of Care Forum Wales which represents independent care providers, said that in a "relatively mild winter we're seeing huge pressures" in Wales and across the UK.
"This should be no surprise to anybody," he said.
"The reality is that we are a million miles away from where we need to be, where we could've been, and we need a wake up call."
The Wales Report is on BBC One Wales at 22:40 GMT on Wednesday 8 February.
Spiralling social care costs cannot be met by increasing council taxes in Wales, ministers have ruled.