Jayda Fransen the former deputy leader of Britain First, has announced she will be standing in the election on July 1 as an independent candidate.
The 35-year-old, who has been convicted of a number of religiously-aggravated crimes, posted a photograph online with St Thomas Church in the background and a white cross in her hand.
In a statement, Nick Baines, Bishop of Leeds, said the Church of England was not consulted over the use of the photograph.
He added: "The Christian Gospel rejects the association of the cross and the church with Jayda Fransen's political statement.
“The church's vision for public life, flowing from the Christian understanding of the life, death and resurrection of Jesus Christ, is one where the common good is served such that all communities, of whatever culture, ethnicity, religion or belief, can flourish together.”
Ms Fransen is one of 16 candidates competing in the election. She is standing against Kim Leadbeater, she sister of Jo Cox, who represented the area until she was murdered by a far-right extremist in June 2016.
Last month, Ms Fransen stood against Scottish National Party leader Nicola Sturgeon when she competed for a seat in the Scottish Parliament, but won just 46 votes.
The July 1 by-election was triggered after Tracy Brabin, who won the seat for Labour in 2019 with a 3,525 majority over the Conservatives, was elected as the mayor of West Yorkshire in May.
The others candidates are: Paul Bickerdike (Christian People’s Alliance), Mike Davies (Alliance For Green Socialism), Therese Hirst (English Democrats), Howling Laud Hope (The Official Monster Raving Loony Party), Susan Laird (Heritage Party); Oliver Purser (Social Democratic Party), Andrew Smith (Rejoin EU), Jack Thomson (Ukip), Jonathan Tilt (Freedom Alliance) and Anne Marie Waters (The For Britain Movement).