The rapper’s teamed up with the artist Molly Crabapple to make the film, which traces the history of the so-called war.
In just under four minutes, he explains over four decades of American drug policy and incarceration.
The video could be signs of him getting increasingly political, after he recently spoke out against the killing of black men by police officers.
The film speeds up Molly Crabapple’s drawings, to whizz through the key points in history.
Jay Z says the war on drugs was started by President Nixon in 1971 and says that at the time the message was: “Drugs were bad, fried your brain.”
He also claims people ignored the failures of politicians for society’s problems.
Instead, “drug dealers were monsters – the sole reason neighbourhoods and major cities were failing”.
In the video for the New York Times, Jay Z says “rates of drug use are as high as they were when Nixon declared this so-called war in 1971.”
He also claims black and Latino people are disproportionately far more likely to be given sentences for drugs offences than others.
“Forty-five years later, it’s time to rethink our policies and laws. The war on drugs is an epic fail,” he says.
In the past, Jay Z has seemed reluctant to get involved in politics or social responsibility, saying his “presence is charity enough”.
But the video may show he’s had a change of heart. Especially after the release of Spiritual, which he put out after the police shootings of killings of Alton Sterling and Philando Castile earlier this year.