The jobless total north of the border now stands at 143,000, fresh data from the Office for National Statistics (ONS) shows.
The Scottish unemployment rate is now 5.2 per cent, slightly above the rate of 4.9 per cent for the UK as a whole.
The statistics also show employment in Scotland increased by 51,000 over the quarter, with the number of people in work now standing at 2,629,000.
The Scottish employment rate increased to 74.1 per cent, slightly below the UK average of 74.5 per cent.
Scottish Secretary David Mundell, said: “I welcome today’s positive figures showing a record increase in the number of people in Scotland in work, and the number of people out of work at its lowest since 2009.
“While we cannot be complacent as we enter a period of adjustment, today’s figures show that we enter the EU negotiations from a position of strength. Our continued priority must still be to work closely with the Scottish Government as ‘team UK’ to promote economic growth.”
• READ MORE: Unemployment total falls by 18,000 to 152,000
Scotland’s Employability Minister Jamie Hepburn said: “There is much to be welcomed from these figures, including 65,000 more people being employed now than at the pre-recession high. However, we know that there is more that we can and must do.
“The Scottish economy has strong fundamentals, but as businesses face uncertainty during negotiations over our future relationship with the EU, we will ensure we work hard to protect Scotland’s relationship with the EU and strive to make the most of current and future opportunities.
He added: “The figures we see published today once again demonstrate Scotland is outperforming the rest of the UK in terms of youth employment. We are determined to do even more and our ambition is to reduce youth unemployment by 40 per cent between 2014 and 2021.
“I am also very pleased that the female employment rate has risen over the quarter. This is a testament to the work we have been doing to ensure women have the same equality of opportunities in the labour market as their male counterparts.
Across the UK unemployment continued to fall in the run-up to Britain’s vote to leave the European Union and there was a record number of people in work.
The employment rate reached a record high of 74.5 per cent, with 31.8 million people in work in the three months to June – 172,000 more than the previous quarter.
A total of 1.64 million people are unemployed – a fall of 52,000 over the quarter and 207,000 down compared with a year ago, giving a jobless rate of 4.9 per cent.
The claimant count, including those on Jobseeker’s Allowance, fell by 8,600 to 763,000 in the period after the Brexit vote between June and July.
However, the claimant count rose by 900 between May and June, the ONS said.