Rt Revd Christopher Foster told peers in the House of Lords the dedication of kinship carers, grandparents, older siblings and other relatives who step in to care for vulnerable children should be recognised.
He warned their "generous and good decision" would be punished by the government if restrictions to the child tax credit are introduced.
The government wants to change the rules under the Welfare Reform and Work Bill so only two children are eligible for the in-work benefit payment.
The Bishop said there were about 200,000 children being raised by kinship carers across the UK, with more than one in five of such families containing three or more children.
"The changes proposed in the Bill with the consequent reduced financial support for these families could well stop potential kinship carers from being able take on the care of a sibling group of children or lead to the splitting of a group of three or more siblings," he warned.
"This is clearly not in the children's best interests, nor in society's or the Chancellor's best interest."
It will cost £30 million to exempt kinship carers from the rules but peers were told the costs to the public purse would be less than if potential carers were put off by the new rules.
Labour's Baroness Sherlock backed the Bishop's call, warning that ministers shouldn't be putting "financial barriers in the way of families willing to take on what are often very vulnerable children".
Work and pensions minister Lord Freud said the Government recognised the vital role that kinship carers played.
But in committee stage debate on the Bill, he acknowledged that he couldn't offer any changes.
It was "fair and proportionate" to limit additional support provided by the taxpayer through child tax credit to two children, he said.
Bishop Christopher also warned that reducing support to larger families would have a "hugely disproportionate impact" on Jewish and Muslim families, who had more children than the national average.
"By limiting financial support to the first two children this policy is making a judgment that touches on deeply personal and strongly held religious and cultural beliefs about the family and that threatens the viability of whole faith communities," he said.
The Bishop urged ministers to examine the potential economic and social impact of the policy on different faith communities.