Large numbers of young people are likely to quit the health insurance market, putting pressure on for more premium rises.
A combination of income hits and health shocks could see young people dropping their cover, the regulator has warned.
Older people tend to make more claims, while younger people are sought after by insurers as they as they are less inclined to make claims.
The Heath Insurance Authority (HIA) said it had set up a special committee to consider the impact the pandemic was having on consumers and the health insurance market.
Average premium costs fell slightly last year when compared with 2018, when there was a price war. But they began to rise from the end of last year.
Now there are fears that health insurers will raise premiums further and restrict which claims they will cover.
The HIA committee will look at the likely impact on the risk equalisation fund.
The fund is to compensate insurers who have older and sicker customers as the law mandates that everyone has to be charged the same premium for the same plan, irrespective of their age or health condition. This is known as community rating.
Chief executive of the HIA, Don Gallagher, said: "As yet, we are uncertain of the impact Covid-19 may have on the market."
He said the combination of the health shock and economic shock as a result of Covid-19 could potentially result in people cancelling their health insurance for a variety of reasons in the short to medium term.
"A significant increase in cancellations at younger ages could potentially impact the sustainability and stability of a community-rated health insurance market," he said.
Health insurance broker Dermot Goode said all three insurers raised their premium costs earlier this year. He said there was now a fear premiums would keep rising this year.
"If upward pressure on premiums continues and if sectors of the economy like hospitality do not recover, then two things will happen: young people will downgrade their cover and others will cancel."
This will put upward pressure on premiums; this is what happened between 2008 and 2012.
He said young people created a "claims buffer" for old health insurance members.
The fears of new premium hikes come as the number of people with health insurance rose for the fifth year in a row.
There are now 2.27 million people who have private health insurance, according to the HIA. The percentage with health cover rose by 2.5pc last year. Almost half of the population, at 46pc, have private health cover.
Premiums per person fell by an average of 0.8pc last year and the year before that when Vhi, Laya and Irish Life Health engaged in a price war.
Prices started to rise at the end of last year and earlier this year.
The average amount paid for a health insurance premium for in-patient cover in 2019 was €1,200. This is down €10 on the average paid in 2018.
Premium income in 2019 was €2.7bn, which represented an increase of 1.4pc on 2018, the HIA said in its annual report.
Market share has not changed, with Vhi at 50pc, Laya Healthcare at 26pc and Irish Life Health at 20pc at the end of December 2019.