A quarter-mile section of the mountain, locally known as Sauce Creek, fell into the sea at the weekend.
Frequented by climbers and walkers, it is part of a pilgrimage route to Mt Brandon, closely associated with St Brendan in the Dingle Peninsula.
Yesterday, Dingle-based Cllr Seamus Cosai called on Kerry County Council to erect signs on approach to the mountain to warn people of dangers.
“People should be told not go too close to the edge,” he told a council meeting in Tralee.
A similar warning was given by John Ahern of South West Walks, who said there had previously been landslides in the area.
Investigations are being carried out by the county council and the Geological Survey of Ireland.
A spokesman said people should use common sense and stay well away from areas where there were obvious fissures and cracks.
A council spokesman said much of Kerry’s 684km coastline was “soft” and sandstone in nature and, therefore, vulnerable to erosion.
However, the council has very little money to deal with the problem which could cost at least €30m to remedy.