It comes after Australian insurer nib, promoted by rugby player Benji Marshall, entered the New Zealand market offering cover for day-to-day medical expenses such as doctors visits, glasses and physiotherapy.
Southern Cross chief executive Peter Tynan said younger people didn't see the need for traditional health insurance, which covered big ticket items such as surgery.
"That age group don't generally have a need for those products or they don't see that need when they're younger, so they don't think its relevant to them."
He said younger people also often had less discretionary income than older people, and saw insurance as unaffordable.
The $1 a day price would be available to those aged up to 34, with those 35 and over paying $1.50 a day. The insurance would cover 75 per cent of health costs, up to annual limits.
Mr Tynan said the move was partly a response to nib coming into the New Zealand market, but it had also been looking for some time at similar products overseas.
"There's an element of that - if these products are going to be attractive to New Zealanders then we'd like to have one in the marketplace with our name on it," he said.
"We're trying to make sure it's the best value New Zealanders can get for it."
Mr Tynan said the need for a mobile app "came strongly across" from the younger market. It would be trialled with HealthEssentials first before being rolled out to other insurance products over time.
The Health Funds Association of New Zealand said overall the number of Kiwis with health insurance has been declining over the past five years, although there were now signs of growth.
A 0.1 per cent rise in the December quarter was the first quarterly increase since June 2009. The overall decline means 60,000 fewer people have health cover than in December 2008. However, total claims paid in the December quarter were the third-highest recorded.
The Southern Cross research was carried out by TRN in September, and had between 1000 and 2000 participants, weighted to be representative of the New Zealand population aged over 15.