362,600 people travelled here, according to new figures from the Central Statistics Office (CSO).
That compares to 227,300 people the previous month.
There was also a 20 per cent increase in the numbers of passengers departing Ireland in August.
However, the CSO says the figures are a small fraction of the numbers that travelled in the same month last year.
In 2019, two million people arrived and departed in August.
Speaking about the recent figures, statistician Gregg Patrick said:
“The Air and Sea Travel Statistics for August 2020 show a very substantial increase in overseas travel compared to the preceding month. In August, 362,600 overseas passengers arrived in Ireland, compared to 227,300 in July, an increase of 59.5 per cent.
"The August 2020 statistics show that continental routes contributed most to the passenger traffic. Some 228,700 passengers arrived on continental routes and 186,000 passengers departed on continental routes."
Mr Patrick also spoke more specifically about the areas people traveled from coming to Ireland. He said apart from Great Britain (which accounts for almost all cross-channel routes), the most important routing countries for arrivals in August 2020 were Spain (33,600), Poland (31,700) and Italy (27,300).
He said those three routing countries were also the most important for departures (after Great Britain), but in a different order; Poland (23,900), Italy (23,300) and Spain (22,800).
"When we look at the year-to-date picture (January-August 2020), the statistics show 3.8 million overseas passengers travelled to and from Ireland.
"This compares to almost 14 million overseas passengers in the same period on 2019, a decrease of almost 73 per cent. This illustrates the continuing and dramatic impact of the Covid-19 pandemic on international travel to and from Ireland," he said.
