The cuts will be the government's first reduction in the public sector workforce of about 700,000 since the financial crisis began, CNN said. Greek public employee jobs are constitutionally protected, the report said.
Public employees have already taken pay cuts of as much as 30 percent and pension benefits have been cut.
Lawmakers voted Sunday to reduce the workforce despite opposition by the civil servants union, CNN said.
The European Union and the International Monetary Fund demanded the cuts as part of an agreement to secure bailout funding.
"We are going through a very difficult path, but this is going to be a success story," Prime Minister Antonis Samaras told reporters after lawmakers voted to cut jobs.
Union officials said the cuts will put an end to Greece's welfare state. About 25 percent of employed Greeks hold government jobs and the national unemployment rate is 27 percent.