Councils are calling for more investment in the sector after the chancellor announced an extra £2bn for social care in England.
But Eluned Morgan said extra money was not enough to address growing demand.
Philip Hammond’s Spring Budget will see an extra £200m spent in Wales over four years as a result of the extra social care cash and other increases.
Finance Minister Mark Drakeford has said the Welsh Government – which has an overall budget of £15bn – will consider how to spend the extra funds.
A recent report by the Health Foundation said that the social care costs for all adults in Wales are set to rise by £1bn to £2.3bn by 2030-31.
Ms Morgan told the BBC’s Sunday Politics Wales programme that creative solutions were needed in the sector.
“I think there’s potential for us to marry here economic development with the care service in the sense that we could be starting to build homes, for example, [that are] adequate for a longer term future for housing older people,” she said.
“We could build an economic strategy behind that.”
She added: “I think we need a creative conversation with the public about what they want [and] how do they want to live when they are older.
“Maybe we can build eco homes where older people won’t be spending a lot of money on heating.”
The Welsh Local Government Association (WLGA), which represents councils, has said that paying for social care is the biggest strategic issue facing local authorities over the next decade.
It has called for money coming to Wales as a result of spending announcements in England – amounting to £150m over three years for day-to-day services and £50m over four years for infrastructure – to be passed on to Welsh councils.
It claims that, if the day-to-day cash was spread evenly, Wales would have an extra £50m a year for services between now and 2020.
WLGA boss Steve Thomas said a big cash injection was needed: “We’ve got a £90m pressure on an annual basis on Welsh social care.
“So even if the whole £50m goes in from Welsh Government from their consequential, it still doesn’t meet the entirety of that pressure.”
Assembly Public Accounts Committee chairman Nick Ramsay said a new way of thinking was needed to address the growing challenge.
“One way or another we need to tackle this because in a few years’ time it may be too late to solve this problem,” said the Conservative AM.
“This can’t be solved overnight, we need to look five, ten years down the line, we’ve got to make sure that we’ve got the right procedures in place so that people in the future can be reassured that they are going to get the social care that they need and, let’s face it, they have paid for.”
Plaid Cymru AM Rhun ap Iorwerth accused ministers of being “far too slow” to act, saying inspiration needed to be taken from “Europe and beyond”.
He said that there needed to be a realisation that an aging population would inevitably lead to a different way of doing things.
“We could put all our money into health and social care and it probably wouldn’t be enough,” he said.
A new body in charge of social care in Wales – Social Care Wales (SCW) – is being formally launched on 1 April.
Chairman Arwel Ellis Owen said social care was being made more sustainable with a greater focus on caring for people at home.
“These are not simple issues, they are very complex issues,” he said.
“But I’m confident that we have here in Wales the tools now to get to grips with the challenge that we’ve got.”