The Scottish Funding Council (SFC) has allocated £10.6m from existing budgets to expand provision in 2013/14 as part of moves to develop higher skills in the workforce.
Professor Sir Timothy O'Shea, principal of Edinburgh University, said the nation's economic future depends on an expansion in the number of Scottish postgraduates. Since 2001, the number of postgraduate students in Scotland – including those from overseas, Europe and the rest of the UK – has risen by 41% from 40,120 to 56,580.
In that period, the number of Scottish postgraduates fell by 1.5% from 26,475 to 26,060.
An SFC spokesman said: "We plan to provide additional taught postgraduate places ... to develop a high-level skills base essential to sustaining the vision of a knowledge-based economy."
Alastair Sim, director of Universities Scotland, which represents principals, said the extra places would help ensure more Scots were able to take up postgraduate courses.
He said: "Scotland's key industries – such as life sciences, energy, finance and business services – need a workforce with the specialist skills and knowledge a postgraduate education provides."
Robin Parker, president of student body NUS Scotland, added: "It's very important to expand opportunities at postgraduate level."
The report warned firms may have to recruit foreign workers or move their offices overseas.