Hunt said an ageing population and a "dementia time bomb" meant helping carers stay in work was an "economic necessity" for the UK.
The health secretary was speaking ahead of the publication this week of a report by the Department of Health, charity Carers UK and organisation Employers for Carers.
The report is expected to claim that £1.3 billion in public money could be saved each year through flexibility.
Hunt said many workers doubled as carers for people with dementia and, with the number of sufferers expected to rise from about 800,000 to more than a million by the end of the decade, employers must help carers stay in work.
He warned large numbers of workers have to give up work to look after relatives and urged employers to act in order to avoid damaging the economy.
Dementia time bomb
"Too many people feel unable to combine caring for a family member with working - this will only get worse as we face the consequences of a dementia time bomb," Hunt said.
"We know that supporting flexible working for parents is good for business and good for the economy - it is time that the same was recognised for carers.
According to the 2011 census, about 6.5 million British workers have caring responsibilities.
Charity Carers UK estimates 2 million of those have given up their jobs, while another 3 million have reduced their working hours.
However, Katja Hall, chief policy director at the CBI, said Hunt's comments are misleading she said employers have embraced flexibility over the past decade.
"The introduction of the right to request flexible working for parents and carers has seen a step-change, based on deals made with the agreement of businesses and parents," she said.
"Businesses have to retain the right to say no, however, as they have to get work done and balance the needs of different employees."
