Church Commissioners, who oversee the organisation's mammoth £8.3 billion investment fund, said on Friday that they "are not as well placed as others" to take a deal forward.
It follows days of talks, spearheaded by the church, aimed at finding a group of buyers for Wonga's £400 million loan book to prevent it falling into the hands of unscrupulous loan sharks.
While it was highly unlikely the church would have been directly involved in the purchase, it had been working to bring a consortium of non-government organisations and philanthropists to organise a buyout.
But the church said on Friday: "The Church Commissioners for England today also confirmed their non-participation in a potential buy-out of the UK loan book having concluded that they are not as well placed as others to take this forward."
It added that "confidential approaches" may now be made by parties from the charitable and finance sectors for the loans.
The church was urged to get involved following intervention from MP Frank Field, who called on Archbishop of Canterbury Justin Welby to find "good people" to buy Wonga's loan book.
Existing borrowers are thought to total around 200,000, and Mr Field said he feared they could be left at the mercy of money lenders and bailiffs who could purchase the debt at a knockdown price.
He said swift action by the church would stop a new lender "terrorising" the poor.
The archbishop said on Friday: "My chief concern has been to ensure that the poor and vulnerable are as well protected as possible following the collapse of Wonga's UK business.
"I fully support and respect the decision of the Church Commissioners not to participate in a potential buy out. They have given this option close attention and I thank them for their time, advice and consideration.
"I will be continuing to examine ways to make affordable credit, debt advice and support more widely available and convening interested parties at Lambeth Palace."
Administrator Grant Thornton is running Wonga's loan book while it looks for a buyer.
In 2013 the archbishop was forced to admit the Church of England's investment fund had invested indirectly in Wonga.
Although the sum was small - about £75,000 out of investments totalling £5.5 billion - he described it as embarrassing.
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