The change, which will mean a reduction in benefits if a household is deemed to have a spare bedroom while claiming housing benefit, will take effect in April this year, meaning thousands in the city will have to find cash for rent previously paid from benefits.
Humza Yousaf, Glasgow SNP MSP and Scottish Government minister said new information has been published showing the extent of the financial impact the change will have on Glasgow.
He said figures from the Scottish Parliament Information Centre show 39% of Glaswegians currently receive housing benefit would be worse off.
Mr Yousaf said: "I am deeply concerned that almost 40% of housing benefit recipients in Glasgow will be punished by this ill-advised, unfair reform.
"People already struggling with other benefit cuts as well as rising food and utility prices will be hit with a penalty which could be over £20 per week.
"This will make a huge difference to so many families in Glasgow and across Scotland."
The MSP said disabled people will also be affected by the changes too
He added: "This tax will also discriminate against people who live in specially adapted social housing.
"Estimates show that 16,000 Scots in socially rented housing who will have to pay extra because of the bedroom tax have an aid or adaptation to their house to assist a household member with a disability.