The hike will cost some families an extra €100. The decision is widely expected to be followed up by other firms.
The premium hikes are being blamed on a new scheme, spearheaded by Health Minister James Reilly, which will allow hospitals to charge insurance firms every time their customers use public beds.
GloHealth, which only entered the market last summer, said the Government decision in Budget 2013 meant it has "no option" but to hike prices.
"The price increases arise from decisions made by the Government in relation to the cost of healthcare. In the recent Budget, the Government indicated that in 2013 it will generate an additional €65m of private income in public hospitals," a spokesperson said.
"There will be higher charges for the use of public beds and other measures taken during 2013, the cost of which GloHealth has no option but to pass on to consumers."
The company, which initially targeted families with young children, said its insurance plans will cost an average of 6pc more from January 30.
This will cost a family of two adults and two children an extra €118 for the mid-level Better plan. The annual cost for this plan will shoot up to €2,098.
Cover is free for children under three from Glo.
Experts have warned that other companies will quickly follow -- with fears that premiums for some customers will rise by up to 50pc.
Dermot Goode, of www. healthinsurancesavings.ie, said Dr Reilly's scheme "will definitely lead to higher premiums".
"Given that the public hospitals will now be able to charge around €1,000 per night instead of €75 per night for these beds, the impact will be significant. There is no doubt that this will be passed on," he added.
The State-owned VHI has indicated that the scheme will see its customers face premium hikes of up to 45pc.