The jobless rate also dropped below that of the whole of the United Kingdom, at 4.7 per cent compared with 4.9 per cent.
The number of people on the claimant count, which includes Jobseeker's Allowance - in August increased by 2,400 to 771,000, the Office for National Statistics said.
The employment rate in Scotland now stands at 74.1 per cent, which remains behind the UK-wide record average of 74.5 per cent.
Some 31.8 million people were in work - up by 174,000 from the previous quarter.
Ongoing improvements in the jobless rate lessens pressure on the Reserve Bank of Australia to deliver further official interest rate cuts, but there are signs that the composition of the labour market is still mixed from state to state.
Office of National Statistics figures show the rate of unemployment in Scotland is now 4.7% compared with the total United Kingdom rate of 4.9%.
Between June and August - a period that included two, post-referendum months - the ONS said job vacancies increased by 3,000 to 752,000.
More news: Obama, Hill leaders meet ahead of federal funding deadline
He went on to say: "These labour market figures continue to show the utmost importance of Scotland and the United Kingdom as a whole retaining membership of the European single market, which will enable us to build on this encouraging progress, and ensure that everyone in Scotland benefits from economic growth".
In considering the contribution of the Census to employment, the ABS confirmed that it will have resulted in an increase in hours that were worked during the month, more than the persons in employment.
However, wage growth in the United Kingdom as earnings, excluding bonuses rose by 2.1% year-on-year against 2.3% growth the previous period and with bonuses was at 2.3% against 2.5% the previous period.
The trend unemployment figure showed a steady labour market, with the jobless rate stuck at 5.7 per cent. "But as inflation is expected to rise further in the coming months, slowing nominal wage growth could mean that consumers soon face real income losses, threatening the consumption-led growth that the United Kingdom has enjoyed for the last couple of years".
However, the number of full-time jobs rose by 11,500, while part-time work fell by 15,400. Capital Economics U.K. economist Ruth Gregory said she expects the labor market to weaken in the months ahead. "We still think there's enough spare capacity in the market to keep inflation low and put pressure on the RBA to lower rates over time", he added.
Wages are rising at 2.3 per cent per year - down on the 2.5 per cent seen last month.
