Unison said figures from Audit Scotland showed there were 1545 under-20s employed in the sector, a drop of 25% since 2009.
Officials fear skills shortages could result, saying that while almost 40% of the public-sector workforce could retire within the next 10 to 15 years, many may leave sooner.
The average age of a public sector worker in the last year was 44 years and four months, up from 43 years and nine months in 2009, according to Unison.
Union chiefs are also concerned the sector could be hit with more job losses, saying 49,500 posts had gone since the financial crash: 4400 last year.
Dave Watson, Unison Scotland's head of bargaining and campaigns, said: "The numbers are staggering and evidence of the disastrous consequences of spending cuts for Scotland.
"The recruitment freeze is already condemning a generation of young people, many of whom have trained for years, to a life of unemployment.
"We are seeing an ageing workforce with well over a third of the workforce due to retire in the next 10-15 years, leading to serious skills shortages."