The amendment also says a High Court judge should adjudicate whether a genocide had actually occurred among those people.
Given the numbers of Christians, Yazidis, Shia Muslims and others who have been displaced by Islamic State for fear of their lives, this would likely lead to Britain's highest court deeming the group's actions as genocide.
For example last year the group released videos appearing to show the murder of 21 Coptic Christians in Libya (immediate below) and also three Assyrian Christians.
Today's vote comes after the US Secretary of State John Kerry and the US House of Representatives voted to declare the jihadist organisation's actions a genocide.
European Parliament made the same declaration earlier this year however the British government has been reluctant to make the same call, saying it is for other international bodies to make such a resolution and not them as an individual national government.
If the Lords amendment passes it would force MPs in the House of Commons to debate and vote on it, putting further pressure on the UK government.
On the weekend a ComRes poll commissioned by the Christian advocacy charity ADF International found most of the British public want the UK government to officially recognise Islamic State's treatment of minorities a genocide.
The ComRes poll found:
63% of the public support the British government officially recognizing the genocide, with 7% opposed.
69% of Britons support the U.K. raising the issue with the United Nations Security Council, with the aim of referring the situation to the International Criminal Court. 7% were opposed.
59% support the U.K. conducting a formal inquiry into the claims that the so-called Islamic State has committed genocide, with 14% opposed.
Baroness Caroline Cox, a Christian peer taking part in the Lords debate, told Premier: "Dietrich Bonhoeffer, the Protestant theologian executed by the Nazis, said silence in the face of evil is itself evil.
"God will not hold us guiltless. Not to speak is to speak, not to act is to act.
"There've been horrendous reports of killings, of rape, of attempts of forced conversion, sexual slavery, gender-based violence, mutilation, forced recruitment of children.
"You can't not care about that horrendous human suffering.
"If the government really does dig its heels in and say no, then I think that would be deeply deeply disturbing and shameful."
Listen to Premier's Aaron James speaking to Baroness Caroline Cox: