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.
Christian refugees fleeing Syria are being bypassed by the UK government, the head of the Roman Catholic Church in England and Wales has said.