The MoD is to switch 50 jobs from the UK National Codification Bureau in Kentigern House, Anderston, to Abbey Wood, Bristol.
However, Glasgow Central MP Anas Sarwar says the MoD's own analysis shows it will cost an extra £50,000 a year to move the jobs.
He said a Value For Money Analysis Report showed the cheapest costed option was to remain in Glasgow and a benefits v risk assessment showed in favour of the city.
He wants Defence Secretary Philip Hammond to come to Glasgow and explain the decision in person to the affected staff.
The workers are involved in sensitive information, cataloguing military equipment for UK and Nato forces.
Mr Sarwar and union leaders said the move should be halted, especially at a time when the UK Government is seeking to reduce costs, not increase them.
He said: "When a leaked MoD report admits relocating these jobs will cost an additional £50,000 a year, the Kentigern House staff deserve to know the MoD's real motivation.
"UK National Codification Bureau staff have performed an outstanding service providing for those who defend our country and it is a real slap in the face that their Government and the MoD have treated them in such a way.
"Staff at Kentigern House deserve an explanation from the minister on why, against all advice, their jobs are a price to be paid for a purpose that they have never been told.
"I hope Mr Hammond will have the decency to come and visit staff to justify or reverse his decision."
Bob Rollings, defence sector group secretary of the Public and Commercial Services Union, said Mr Hammond was not made fully aware of all the facts associated with the move.
He said: "This is a scandal. These highly professional and dedicated workers, who have received numerous plaudits for the quality of their work over the last 26 years, are being treated with contempt.
"This relocation will mean the loss of key specialist skills, with a detrimental effect on frontline supplies.
"The Government claims to want to save money from the public purse, yet here is a plan that will increase costs.
"We also believe the minister was not informed of the risks associated with this proposed relocation, so PCS is asking this absurd decision is immediately reversed with the jobs retained in Glasgow."