On September 28, 2018, a large earthquake and its accompanying tsunami waves caused severe damage to the coastal area of Palu Bay, in the central western part of Sulawesi Island, Indonesia. To clarify the distribution of tsunami inundation and run-up heights, and damage to coastal communities due to the tsunami, the authors conducted a field survey 1 month after the event. In the inner part of Palu Bay tsunami inundation and run-up heights of more than 4 m were measured at many locations, and severe damage by the tsunami to coastal low-lying settlements was observed. In the areas to the north of the bay and around its entrance the tsunami inundation and run-up heights were lower than in the inner part of the bay. The tsunami inundation distance depended on the topographical features of coastal areas. The southern shore of the bay experienced a longer inundation distance than other shores, though generally severe damage to houses was limited to within around 200 m from the shoreline. The main lessons that can be learnt from the present event are also discussed.