The Church of Scotland, the Baptist Union, the Methodist Church and the United Reformed Church said the cap would hit children the hardest.
The churches believe the number of Scottish families with capped benefits will increase by more than 10 times.
The Department of Work and Pensions described the benefits cap as "a clear incentive to move into a job".
Ministers said the level of the cap was fair because it is close to the average salary after tax.
The new rule means families can now receive no more than Â£20,000 a year - down from Â£26,000.
The cap relates to a string of benefits for those aged 16 to 64 including child tax credit, housing benefit, jobseeker's allowance and income support, but excludes some others such as disability living allowance.
Households where someone works more than 16 hours a week are exempt.
The churches said the cuts were "manifestly unfair".
Rev Dr Richard Frazer, convener of the Church of Scotland's Church and Society Council, said: "Eleven thousand Scottish families, almost all with children, face being affected by the new benefit cap.
"We know, from our experience on the ground and the UK government's own research that the benefit cap drives people into rent arrears, debt and hunger."
Dr Frazer described the cap as punishment for hundreds of children and said those who carried the heaviest burden were the "least able to suffer it".
"We cannot tackle poverty by making people poorer and we cannot leave families without enough to meet their basic needs," he added.
Paul Morrison, policy officer for the Methodist Church, said: "Over 2,000 single parents with babies under a year of age had their housing benefit cut because of the cap each month.
"Does the government seriously expect that cutting housing benefit will make it easier for them to find work?"
But a Department for Work and Pensions spokesman said: "We are committed to helping lone parents into a job which fits in around their caring responsibilities, which is why we are doubling the amount of free childcare available.
"We know that work is the best route out of poverty, and there are now record numbers of lone parents in work.
"The benefit cap provides a clear incentive to move into a job, even if it is part time, as anyone eligible for working tax credits is exempt."
A UK benefits cap that has just come into force is "indefensible", church leaders in Scotland have said.