The Office of Public Works has advised people to book well in advance to visit Sceilg Mhichíl as it opens for the summer.
Bad weather had postponed the opening of Sceilg Mhichíl last Sunday, but the first few visitors started arriving yesterday.
OPW staff had been unable to leave the island from last Sunday.
Frank Shalvey, of the OPW Heritage Service, told RTÉ's Morning Ireland that those looking to visit the island this weekend had "slim" chances.
Mr Shalvey, of the OPW Heritage Service, confirmed that the average price of a trip to the UNESCO site is around €60.
However, he said that the OPW do not set the price or charge admission. The OPW pick and regulate the boat companies.
Mr Shalvey confirmed that a rockfall that happened earlier on this year has now been disposed of.
The number of visitors to the island is limited by the OPW, which has licensed 15 ferry operators to carry 12 passengers on each trip to Sceilg Mhichíl everyday.
An estimated 14,000 people will visit the island between now and 2 October when it will be closed again.