A police officer cordons off the scene in Wexford
Five other refugees were taken to hospital after the discovery near Wexford.
Police said the dead were six men and two male children. They are understood to be Romanian.
A spokesman for Wexford General Hospital said following treatment they would require emotional assistance because of their ordeal.
The find follows the deaths of 58 Chinese refugees who suffocated in a lorry in Dover, south-east England, in June last year.
Irish Premier Bertie Ahern said it was an appalling tragedy and pledged to track down the criminals responsible.
"Those involved in the cruel trade of trafficking in human beings have perpetrated yet another atrocity on the victims of their greed," he said.
Business complex
Irish police said the shipping container was found at the Drinagh Park business complex just outside Wexford town.
The container began its journey in Italy and arrived in the Irish Republic on the ship Dutch Navigator.
The ship left Zeebrugge, in Belgium, on Tuesday evening and arrived in Waterford in Ireland at 2300 GMT on Thursday.
Sealed off
The container, believed to be carrying furniture, was held overnight at the quayside and departed at 0815 GMT on Saturday for delivery in Wexford town.
Upon arrival, the driver detected movement and alerted the police.
The scene was sealed off and officers from the Irish police force's National Immigration Bureau were called in.
Irish police described it as "a nightmare of human misery".
They are "actively investigating" the likelihood that the 13 had been packed into the container after paying traffickers in European refugees to organise their journey.
The driver and his colleague had to be treated in hospital for the shock of finding the bodies.
The Irish Refugee Council said it was deeply shocked by the deaths.