Education Ministry officials could not be immediately reached for comment on the union estimate.
Under government plans, 25,000 public sector employees are to be suspended this year and 15,000 will be fired in the next 15 months as part of efforts to trim Greece's bloated public sector and to meet conditions of the country's international bailout.
Greece has been depending on rescue loans from the International Monetary Fund and other European countries that use the euro currency since May 2010. In return, it has imposed repeated rounds of austerity measures, slashing salaries and pensions and introducing rounds of tax hikes.
While Greek budget figures are showing some signs of improvement, with the budget deficit narrowing, the measures have also left the economy hammered by a deep recession, now in its sixth year. Unemployment has spiraled to above 27 percent, and is nearly 60 percent for those under the age of 25.
Conservative Prime Minister Antonis Samaras renewed a promise to end the recession next year.
"We are not out of the woods yet," he told a conference in central Athens. "But in the last 14 months, we've changed the image of our country abroad. We've stabilized our country internally. We have implemented sweeping reforms and brought our program back on track."