Archbishop of Westminster Vincent Nichols said Christians were the most persecuted people, but few of them would receive sanctuary in the UK.
The government has said 20,000 refugees will be brought to Britain directly from refugee camps around Syria.
But Cardinal Nichols said most Christians did not go into the camps.
Speaking on BBC Radio 4's Today, Archbishop Nichols said: "I can see the point in going directly to the refugee camps, but in fact I think its unintended consequence will be that there will be few, if any, Christians coming to this country.
"That is because for the most part Christian refugees do not go into the UNHCR (United Nations High Commissioner for Refugees) camps. They go to fellow Christian organisations."
He added: "If we are going to deal purely with UNHCR according to their rules, then there can be no preference given to anybody on behalf of their faith and we will simply bypass the Christian refugees, not intentionally but in fact."
It comes as the Archbishop of Wales, Dr Barry Morgan, will say that Britain has lost its sense of proportion in relation to the refugee crisis.
In his Christmas sermon at Llandaff Cathedral in Cardiff he is expected to say that the "debate seems to be centred on how many refugees we should accept. We forget to ask, or perhaps we choose to forget, why there are so many refugees in the first place".
The refugees being brought to the UK will be drawn from established refugee camps, initially as part of the Vulnerable Persons Relocation (VPR) scheme.
More than 50 local authorities have taken a share of those who have already arrived.
Alongside the VPR scheme, the UK has also granted asylum or other forms of protection to 1,868 Syrians in the year ending September 2015.

The PRI is set to win about 30%, with the conservative National  Action Party on about 22%, said the head of the National Electoral Institute.
On current projections, the PRI will see its number of seats drop slightly.
The run-up to the poll was marked by violence with drug cartels blamed for the deaths of several candidates.
On Sunday morning, protesters and parents of 43 students who disappeared last year burned election material in the town of Tixtla.
They say they want answers about what happened to the students before elections are held.
A dissident teachers' union also burned ballots and ransacked offices of political parties to express its anger at education reforms.
Ahead of the elections, there was a great deal of pessimism - the feeling among many that votes do not really matter, politicians here are all the same, and violence will continue no matter what.
But at a polling stations on Sunday, in relatively peaceful Mexico City, there was a sense of duty among many - that voting was the only way to make a difference. Asked what their main concern was and almost without exception, the response among voters was: 'Security.' People here are worried about where the country is heading.
Despite President Pena Nieto's promises to restore peace in Mexico, these elections have proved otherwise. They have been some of the most violent in recent history.
President Pena Nieto deployed federal police and troops to guard polling stations.
His spokesman Eduard Sanchez said on Saturday: "Mexicans have the right to vote in peace... [we] will take all necessary measures within the framework of legality'' to protect the elections.
Ahead of the polls opening, the CNTE teachers' union attacked the offices of five political parties in Chiapas state in the south of the country.
In Guerrero state, explosive devices were thrown into a conservative party's office.
Meanwhile in Oaxaca, as well as Guerrero, tens of thousands of ballot papers were burnt by protesters.
A former mayor was shot dead outside a polling station in the same state.
A number of candidates and numerous campaign workers have also been killed in drug-related violence.
Christian refugees fleeing Syria are being bypassed by the UK government, the head of the Roman Catholic Church in England and Wales has said.
[NEXT_CONCEPT]
Mexican President Enrique Pena Nieto and his Institutional Revolutionary Party will keep control of Congress, preliminary election results suggest.