The number of properties for sale here has hit a nine-year low, according to the website DAFT.ie.
At less than 24,000, it is at its lowest point since February 2007.
The biggest falls in availability are now outside Leinster.
Across Munster, Connacht and Ulster there were 13,500 homes for sale in April 2016 compared to 21,000 just two years previously.
Prices are reportedly rising because the increase in population each month is not being matched by an increase in new homes.
Ronan Lyons, a Trinity College economist who compiled the survey, says there is a two-tier market emerging.
He said: "Prices now are basically stable in the capital, in the last two years they have only increased by 1% on average and in fact in some postcodes prices are now falling.
"In the rest of the country though, it's a bit like Dublin was a couple of years ago because we have got accelerating inflation in house prices.
"If you look at Cork city or Galway city there you've got prices rising by 15% to 20% year-on- year."
Cork saw prices for the first quarter of 2016 rise 14.9% higher than the same period last year.
In Galway house prices were up 14% compared to 2015 while Limerick and Waterford recorded 18% price hikes.
In Dublin, prices have risen by about €91,000 or 41% - from their lowest point in mid-2012 while elsewhere the average increase has been €37,500, or 28%, since the end of 2013.
The figures show that house prices have risen by almost 6% during the first quarter of this year.
The average asking price now stands at €210,000 compared to €198,000 a year ago, according to the latest report from property website Daft.ie.
Mr Lyons said: "It is interesting to note that in year-on-year terms, prices are now falling in five Dublin markets - Dublin 2, Dublin 6, Dublin 16, Dublin 18 and South County Dublin.
"These are some of the most expensive markets in the country and show the effectiveness of the Central Bank rules. Nonetheless, across the country, prices continue to rise, because the increase in population each month is not being matched by an increase in new homes.
"Addressing the shortage of supply - in particular the high cost base on construction - must a top priority for the new government."
