It says it is trying to stop a "culture of working overtime".
South Korea has some of the longest working hours in the world.
Government employees there work an average of 2,739 hours a year - about 1,000 hours more than workers in other developed countries.
The shutdown initiative in the Seoul Metropolitan Government is set to roll out across three phases over the next three months.
The programme will begin on 30 March, with all computers switched off by 20:00.
