This is a marked slowdown from the high growth of 0.6%, revised down from 0.8%, which the economy north of the border enjoyed in the first three months of this year.
The wider UK economy grew at three times the Scottish rate, with growth of 0.3% in the second quarter.
The Services sector grew by 0.7% in the latest figures, but output in Production fell by 0.7% and output in the Construction sector fell by 3.5%.
Scotland's economy has struggled since the North Sea downturn in the aftermath of the global oil price crash. In the final quarter of last year the Scottish economy shrank by 0.2%, but the country avoided recession with the booming growth in the early part of this year.
Secretary of State for Scotland David Mundell said: “Scotland’s economy still lags behind that of the rest of the UK, and it is more important than ever that Scotland’s two government’s work together to improve Scotland’s economy.
“The UK Government is investing in Scotland, through support to our oil and gas industry, UK City Deals and our ambitious Industrial Strategy. Now the Scottish Government needs to use the considerable levers they have to increase Scotland’s prosperity.”
Scottish Government economy secretary keith welcomed the second successive quarter of growth.
“Although this is more modest growth than we would ideally like to see, it is particularly pleasing to see growth over the first half of the year in industries linked to the oil and gas supply chain, which provides more evidence that confidence is gradually returning to the sector,” he said.
“Additionally we are seeing strength in Scotland’s services sector – which is particularly good news given that it is by far the largest part of the economy in terms of turnover, value added and employment.”
He put the slump in construction down to major building projects, like the Queensferry crosing, having been completed, but insisted mnisters are still planning £4 billion of investment in new schemes this financial year.
Labour’s economy spokesperson Jackie Baillie said the figures are “anything but good news.”
“They show almost no growth in the Scottish economy, and particularly disappointing figures for the construction industry – which has seen a three and half per cent fall,” she said.
“Year-on-year we lag behind the rest of the UK’s growth, which itself is nothing to crow about, with Scottish economic growth a third of the UK as a whole.”
Professor Graeme Roy, director of the Fraser of Allander economic think tank at Strathclyde University, said that five of the last six quarters have now witnessed Scottish growth of just 0.1% or lower.
“Over the year, the Scottish economy has grown around 1/3 of the equivalent UK rate,” Prof Roy added.
“The one significant bright spot was the strength of Scotland’s services sector which grew +0.7% over the quarter with financial and business services growing strongly both over the quarter and the year. Construction continued to decline - for the sixth consecutive quarter - whilst manufacturing also slipped back a little.”