Over the weekend, hundreds of families fled Mosul, a once-cosmopolitan city that is the country's second largest.
In a unanimous declaration adopted late Monday, the Council's 15 member countries condemned "in the strongest terms the systematic persecution of individuals from minority populations and those who refuse its extremist ideology in Iraq by ISIL and associated armed groups," it said, referring to the group's former name of Islamic State of Iraq and the Levant.
"The members of the Security Council further recall that widespread or systematic attacks directed against any civilian populations because of their ethnic background, religious beliefs or faith may constitute a crime against humanity, for which those responsible must be held accountable."
The Council also asked that the Iraqi government and the United Nations intensify their efforts to serve the "urgent" humanitarian needs of people displaced by the conflict and to tackle the "terrorist threat" against minorities.
On Sunday, the militants took over the fourth century Mar (Saint) Behnam monastery in northern Iraq, one of the country's best-known Christian landmarks, and expelled its resident monks.
Christians abandoned their homes and belongings in Mosul after IS fighters running the city issued an ultimatum for Christians to convert, pay a special tax, leave or face the sword.
Before the 2003 US invasion, more than a million Christians lived in Iraq, including more than 600,000 in Baghdad and 60,000 in Mosul, as well as a substantial number in the oil city of Kirkuk and in Basra.
Until their forced exodus over the weekend, Christians had been continuously present in Mosul for about 16 centuries.