There are fears a second major rockfall on Sceilg Mhichíl could delay the opening of the Unesco World Heritage site.
A team from the Office of Public Works and a number of Safety Contractor workers have arrived on the island to assess the damage.
In a statement, the OPW said winter storms and instability caused by rabbits burrowing under dry rocks seem to be the cause of the rockfall, rather than filming activity or extra visitors to the site.
Sceilg Mhichíl is the setting for part of the latest Star Wars series and filming was carried out there in 2014 and 2015.
It features strongly in the official trailer for the next instalment - Star Wars: The Last Jedi.
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The most recent rockfall occurred on the island's roadway near the lighthouse and away from the main visitor path.
The site is due to re-open on 14 May, but the OPW said: "At this point, was not possible to be definitive about the opening date . . . but the OPW remain cautiously optimistic that it will be achieved".
Senior Conservation architect Michael Grellan Rourke said rockfalls on the island were common, although this was only the second major such incident in 40 years.
However, he rejected any suggestion the rockfall was linked to increased visitor numbers or to filming.