Overall welfare spending will be kept to £119.5 billion for the first year of the next Westminster Parliament. The cap covers all welfare payments except the state pension and benefits linked to cyclical unemployment rates, principally Job Seekers' Allowance.
Maureen Watson, head of policy at the Scottish Federation of Housing Associations (SFHA) said it took no account of the impact of the so-called 'bedroom tax,' which cuts the amount of housing benefit that people can receive if they are deemed to have a spare room.
In January, the SFHA said its 160 members could expect to face a bill of almost £80 million over three years as tenants were forced to downsize. It predicted this would include lost rent and tenancy charges as thousands look to move to smaller homes.
Ms Watson added: "Measures such as the 'bedroom tax' will actually end up costing the public purse more. This is partly because it risks forcing social tenants into the private sector, where rents are higher, and partly due to the extra costs for councils and housing associations.
"We call upon the UK Government to exclude housing benefit from the envelope of welfare benefits being capped."
Mike Turley, head of public sector at Deloitte, said the cap was "an important step in tackling a long-term pressure on public finances". He said welfare currently accounted for 29% of public spending but partly agreed with the SFHA's view on costs, adding: "Care does need to be taken to ensure that capping welfare spending does not lead to increased costs elsewhere."
Children's Society chief executive Matthew Reed said: "Applying an arbitrary cap to welfare spending takes no account of changing circumstances of families caught up in poverty facing rising living costs beyond their control, including childcare and rocketing rents."
Alison Garnham, chief executive of the Child Poverty Action Group, said the Budget "tries to lock in austerity for millions of low-paid families, poor children, carers and disabled people".
Save the Children's William Higham, said: "If the welfare cap is mishandled and pushes low-income families further into poverty, it risks children's life chances."