The Public and Commercial Services (PCS) union also said thousands of other members of staff are at risk of redundancy when other sites are transferred to new premises by June 2023.
DWP minister David Rutley told MPs that meetings were being held with affected staff yesterday.
Some 3,000 jobs within the DWP could be at risk from the plans to close offices, MPs heard.
SNP work and employment spokesman Chris Stephens said: “Can the minister confirm that the announcement could mean 3,000 job at risk of redundancy in the Department of Work and Pensions? And what measures is he going to ensure that this does not happen?”
He also claimed the DWP is “looking to close offices in high economic deprivation areas” which is “counter-intuitive to the so-called levelling-up agenda”.
Mr Rutley replied: “There are going to be around 12,000 colleagues who will be moving from one site to another in close proximity – around 28 sites involved there.
“In terms of colleagues that will be affected where there is no other strategic site nearby, there are around 1,300 colleagues that could be involved.”
Mr Rutley added that the Government will “see what opportunities there are within DWP” and other departments for affected staff and added that the change “does not impact job centres and the customer-facing interactions”.
PCS general secretary Mark Serwotka said: “The Government was quick to clap civil servants at the start of the pandemic – they’re even quicker to scrap them now they’ve declared the pandemic over.
“Our members have worked tirelessly behind the scenes, keeping the country running, paying out benefits to almost two-and-a-half million families, helping them to put food on their table and keep a roof over their head.
“These are the workers rightly praised in November last year by Prime Minister Boris Johnson as ‘miracle workers’.
“But now, as food and fuel prices rise faster than ever, they’re being abandoned by the Government and left to fend for themselves.”
Jonathan Ashworth, shadow work and pensions secretary, said: “In closing DWP offices and cutting jobs in areas including Stoke, Burnley, Bishop Auckland, Doncaster, Southampton and Kirkcaldy, Therese Coffey (Work and Pensions Secretary) has exposed the Tories’ rhetoric on levelling up to be utterly hollow.
“Ministers are today cutting quality public sector jobs from communities who need them in the middle of a devastating cost-of-living crisis.”
A Government spokesman said: “As part of plans to improve the services we deliver to claimants, help more people into employment and modernise public services, DWP is moving some back office staff to better, greener offices, which will not affect any public-facing roles.
“This is not a plan to reduce our headcount – where possible, our colleagues in offices due to close are being offered opportunities to be redeployed to a nearby site, or retrained into a new role in DWP or another government department.
“We are making every effort to fully support our staff through this process.”