The jobless rate in May was the lowest reading since May 2011.
Seasonally adjusted data showed the number of unemployed at 815,166 people, with younger persons aged up to 24 bearing the brunt of being out of work.
Among younger persons aged 15 to 24, the jobless rate fell to 33.8pc from 38.9pc in the same month in 2018.
Greece's jobless rate, which hit a record high of 27.8pc in September 2013, has been falling since but remains the highest in the euro zone.
In its spring forecasts, the EU Commission expects some slowdown in Greece's labour market recovery due to a recent increase in the statutory minimum wage. It projects a jobless rate of 18.2pc this year.
Greece's economy expanded in the first quarter, driven by consumer spending and a pick-up in investments, although a slow-down in Europe made falling exports a drag.