Margaret Burgess also told the social landlords to look at re- classifying rooms used by disabled people to store equipment so that they are not deemed a spare bedroom.
The new Under Occupancy Rules, known as the 'bedroom tax', are due to take effect on April 1 and will mean homes considered to have one 'spare' bedroom will lose 14% of their housing benefit and two or more 'spare' rooms will face a 25% cut.
More than 100,000 households in Scotland are estimated to be affected, and the UK Government has been warned people will be trapped into losing benefit cash as there are not enough, smaller properties available for people to downsize to.
Dundee City Council has already said it will not evict tenants who run up arrears as a result of the benefit cut.
As well as tenants being unable to avoid a cut in benefit through moving, Ms Burgess said there was insufficient and disproportionate help coming to protect those who can't afford to pay.
She added: "The Department for Work and Pensions' answer to this is Discretionary Housing Payments (DHPs).
"However, this is inadequate in Scotland. By DWP's own analysis, London and Scotland will have the same number of people affected by the bedroom tax.
"However, London is set to receive £56m in DHPs while Scotland will receive £10m."