The men fell while carrying out works on a shed roof at a farm in Ardagh in west Limerick.
The HSA said the main hazards when working at height are falls from ladders, unprotected edges of roofs and falls through fragile roof materials.
Gardaí and the HSA are investigating the fatal incident, having been alerted to it on Tuesday morning.
Speaking at Tullamore Show, Minister Martin Heydon said challenges in the area of farm succession are affecting farm safety.
It is understood that a member of staff was injured during last Wednesday's sale in Portumna Mart.
The 10-year-old lost his life at the weekend following a fatal farm incident.
Both stacking bales and slurry gas are lethal on farms and individuals must take safety guidelines into consideration.
Farmers must take particular care with older people and children on farms as they collectively account for 55% of farm fatalities.
The HSA is aiming to reduce the risks associated with forestry work, including handling machinery, working at height, chainsaw use, and emergency response planning in new inspection campaign.