The rapper claimed that the late singer was such a force on the rock scene in the early '90s that he temporarily stopped the hip-hop movement.
"'Hair bands' dominated the airwaves and rock became more about looks than about actual substance and what it stood for - the rebellious spirit of youth," Jay-Z says in Pharrell Williams's new coffee table book Pharrell: Places and Spaces I've Been, as reported by Spin.
"That's why 'Teen Spirit' rang so loud because it was right on point with how everyone felt."
He continued: "I have always been a person who was curious about the music and when those forces come on the scene, they are inescapable.
"Can't take your eyes off them, can't stop listening to them. [Cobain] was one of those figures. I knew we had to wait for a second before we became that dominant force in music."
He added: "It was weird because hip-hop was becoming this force, then grunge music stopped it for one second, ya know.
"Those 'hair bands' were too easy for us to take out; when Kurt Cobain came with that statement it was like, 'We got to wait a while'."
Jay-Z recently announced plans to release a new live EP titled Live in Brooklyn, which was recorded during his residency at the new Barclays Center in Brooklyn, New York.
Pharrell: Places and Spaces I've Been is released on October 16.
Watch the music video for Nirvana's 'Smells Like Teen Spirit' below: