The US evangelist is due to host a mission event at the city's FLYDSA arena as part of an eight day tour next June.
The Rt Rev Dr Pete Wilcox released a statement on Wednesday encouraging churches not to attend on the grounds that Graham's views "represent a risk to the social cohesion of our city".
The statement read: "I'm afraid I cannot support the Graham Tour mission event at the FlYDSA Arena on 6th June next year, at which Franklin Graham is due to speak, and so will not be encouraging parishes in the Diocese of Sheffield to support it either.
"Mr Graham's rhetoric is repeatedly and unnecessarily inflammatory and in my opinion represents a risk to the social cohesion of our city.
"I gladly took part in Billy Graham's Mission England in 1984 as a candidate for ordained ministry, and in his LiveLink Mission in 1989 as a curate. But to my sadness I detect a tailing off of humility and generosity in the Graham organisation since those days."
The son of legendary Billy Graham held a rally in Blackpool last year in which thousands attended, his visit was met with objection though with a petition calling for him to be banned from entering the country due to past comments on Islam and homosexuality.
The preacher has previously described Islam as "an evil and very wicked religion" and spoken out against LGBT rights, saying Satan is behind same-sex marriage.
The Billy Graham Evangelistic Association have declined to comment.