The rapper says the strict anti-narcotics laws introduced in the 1980s unfairly targeted minorities.
In the four-minute video, he also argues that "young men like me who hustled became the sole villain, and drug addicts lack moral fortitude".
Jay Z, who was born Shawn Carter, has frequently rapped about his past as a crack dealer.
In the illustrated film, the 45-year-old musician suggests punishment of drug dealers is hypocritical given that states such as Colorado have legalised marijuana.
He points out white businessmen are profiting off the decriminalised cannabis trade, while black men with jail records are barred from participating in the industry.
"Why are white men poised to get rich doing the same thing African-Americans have been going to prison for?" he says.
He also blames the sharp rise in the US prison population on mandatory minimum sentences.
The video goes through the history of the drug war, and how it has "disproportionately come to lock away blacks and Latinos".
Jay Z has rapped in many of his songs about his own drug-dealing past in New York City's Brooklyn borough.
Jay Z has declared the decades-long US war on drugs an "epic fail", in a short film he wrote and narrated.