The charity said that it could no longer support the Home Office scheme because it was "concerned about its compulsory nature".
The scheme had been under pressure from churches and refugee groups, in particular the No One Is Illegal campaign group, which has dubbed it "immigration slavery" and likened it to community service for offenders.
Section 10 of the Immigration and Asylum Regulations 2005 requires failed asylum seekers, banned from taking regular paid work, to carry out "community activities" in return for food and accommodation. Those who refuse lose support.
Richard Capie, spokesman for YMCA England, said: "There was concern at the compulsory nature of the legislation. We have decided to run a pilot elsewhere only if it is voluntary, and we are still in discussions with the Home Office over that possibility."
The charity had provisionally agreed to run the scheme in Liverpool.
"Our intention was to run a pilot that would focus on the needs of the individuals involved," said Capie. "Our consultations with community groups in Liverpool have demonstrated that this is not possible."
A Home Office spokesman said: "The pilot scheme is not designed as a punishment."