The UK government says there won't be any exemption given for clergy under new plans to lower migration levels.
New plans unveiled by Home Secretary James Cleverly on Monday state that skilled workers coming from overseas must be paid a minimum of £38,000.
That would rule out a large number of church workers who come to the UK to serve.
Raising the issue in the House of Lords on Tuesday, Bishop of Norwich Rt Rev Graham Usher said: "Many faith communities greatly benefit from the presence of religious workers from overseas.
"The Church of England benefits from the ministry of clergy from all around the Anglican Communion, enriching our communities and resourcing individuals’ ministry for life, often equipping them for when they return to their country of origin to minister in places of conflict and abject poverty.
"Many UK clergy, me included, have benefited from overseas experiences.
"Will the Minister consult faith communities about exemptions for religious workers, many of whom earn below the published threshold?"
Responding on behalf of the government, Lord Sharpe said: "Of course, there is no barrier to recruiting people to the Church, as long as £38,700 is paid to them.
"I do not think that unreasonable, I am afraid. I appreciate that salaries may not be as high in the Church as he might like, never mind the rest of his colleagues, but that is the median salary, as I said earlier, and it is not unfair."
The Home Secretary has said the changes will slash the number of people coming to the UK by 300,000 a year.