The Iraqi Government-supported Shia militias receive arms from at least 16 countries, including the UK, the US, Russia and Iran, according to the human rights organisation.
The report claims that paramilitary militias operate as part of the Iraqi armed forces to combat ISIS.
It also argues that militias use Iraqi military arms to commit war crimes, revenge attacks and other atrocities.
Amnesty International UK arms control director Oliver Sprague said: “The Shia militias’ reign of terror is being enabled by a vast arsenal of weaponry eagerly supplied by the Baghdad government.
“The UK must urgently spell out what measures it has in place to make sure weapons it sends to Iraq don’t end up in the hands of abusive Shia militias.
“UK ministers like to talk about how their support for the Iraqi forces is taking the fight to ISIS, but they’re silent on the multiple atrocities committed by the Shia militias.
“How can we be sure that the weapons we send to Baghdad aren’t be used by vengeful Shia militias right now to kill civilians in and around Mosul?”
The UK recently supplied at least 800 machine guns and 550 sniper rifles to the Iraqi Government.
In addition, the British Government presented weapons worth around £2m to Kurdish Peshmerga forces between 2014 and 2015.