Members of the Public and Commercial Services union plan to strike for a week, followed by 'work to rule' when they return.
The workers have already taken a series of stoppages over the summer over plans to close the office in Eastern Avenue, Arbourthorne, as part of a Government cost-cutting drive which would see one in 10 job centres close to save Â£140 million a year.
The PC' union’s 50 members say securing the future of the job centre is vital for unemployed, sick and disabled people in one of the most deprived areas of the city and that forcing claimants to travel would make it harder for people to access employment and training opportunities.
PCS general secretary Mark Serwotka said: "PCS is pleased to have the support of the whole trade union movement against job centre closures, and welcome the support that Jeremy Corbyn and all Sheffield's Labour MPs have given to date.
"Now is the time for the Government to rethink their plans and stop this closure."
A Department of Work and Pensions spokesman said: "The changes we are making to our estate across the country will offer a more efficient service, and deliver good value for the taxpayer, saving over Â£140 million a year, for the next 10 years."