Alex Salmond will raise objections to the UK welfare reform with David Cameron at a meeting of the heads of the UK administrations on Wednesday.
The under-occupancy charge, described as a bedroom tax by its opponents, will cost the average tenant £54 a month if they do not fill the room or move to a smaller property.
Those affected can apply for discretionary housing payments to help with their rent in some circumstances, including those in disabled-adapted homes or in an area with a shortage of shared accommodation.
The Joint Ministerial Committee (JMC), which is made up of the leaders of UK Government, the Scottish Government, the Welsh Government and the Northern Ireland Executive, meets once a year.
Scottish Youth Employment Minister Angela Constance will accompany the First Minister to this week's session of the committee.
A Scottish Government source said: "The bedroom tax is a deeply unfair, deeply unpopular policy, and its full effects are now becoming clear in communities right across Scotland.
"It affects around 82,000 social rented-sector tenants in Scotland, who are losing around £50 per month or £600 a year. Around 80% of those households include a disabled adult, and around 15,500 families with children in Scotland are being penalised."