Writing in the Sunday Telegraph Lord Carey has said oil-rich Gulf States should be "doing more" to help stem the flow of refugees and migrants from the Middle East.
The former archbishop has also called for British military involvement against Islamic State in Syria, as David Cameron reportedly hopes to persuade Labour MPs to back airstrikes against Islamic State in Syria in a Commons vote next month.
Prime Minister David Cameron has said the UK will take "thousands" more refugees who have fled fighting in Syria and are in UN camps in neighbouring countries.
Mr Cameron has been under pressure in recent days to provide sanctuary for those escaping the long-running Syrian civil war.
"Some will not like me saying this, but in recent years, there has been too much Muslim mass immigration to Europe. This has resulted in ghettos of Muslim communities living parallel lives to mainstream society, following their own customs and even their own laws, wrote Lord Carey.
"Isn't it high-time instead for the oil-rich Gulf States to open their doors to the many Muslims who are fleeing conflict? Surely if they are concerned for fellow Muslims who prefer to live in Muslim-majority countries, then they have a moral responsibility to intervene," added Carey.
Lord Carey also suggested Britain should prioritise persecuted Christians fleeing conflict in the Middle East, saying they were currently being left "at the bottom of the pile" by the international community.
"They are the most vulnerable and repeatedly targeted victims of this conflict. Indeed, a hundred years after the Armenian and Assyrian genocide, in which over a million Christians are estimated to have been killed by Ottoman Muslims, the same is happening today in the form of an ethnic cleansing of Christians in the region. Christians have been crucified, beheaded, raped, and subjected to forced conversion. The so-called Islamic State and other radical groups are openly glorifying the slaughter of Christians.
He said: "Britain should make Syrian Christians a priority because they are a particularly vulnerable group. Furthermore, we are a Christian nation with an established Church so Syrian Christians will find no challenge to integration. The churches are already well-prepared and eager to offer support and accommodation to those escaping the conflict.
The former Archbishop also appeared to back renew efforts to launch British military intervention against Islamic State in Syria.
"It's not enough to send aid to refugee camps in the Middle East. There must be renewed military and diplomatic efforts to crush the twin menaces of Islamic State and al-Qaeda once and for all. Make no mistake: this may mean air strikes and other British military assistance to create secure and safe enclaves in Syria," said Lord Carey.