Islamic State has executed several hundred of the people west of Mosul, according to officials.
The Yazidi Progress Party said 300 captives were killed on Friday in the Tal Afar area.
Cardinal Vincent Nichols said: "I am deeply shocked by the brutal murder of these peace-loving people.
"The Yazidis I met in our recent visit to Erbil impressed me with their quiet dignity.
"I am sure that all people of decency will condemn these killings.
"I commend those who have been killed to the mercy of God and I pray earnestly for the peace of the region."
Yazidis take various elements of other religions to form their lifestyle but are seen as infidels by Islamic State.
IS militants have been persecuting the group, along with Christians, as they advance across parts of Iraq and Syria.
Experts say the jihadis often have more contempt for the Yazidis than Christians.