Nicki Minaj says her “precious cousin” was shot and killed in Brooklyn yesterday … and TMZ has learned the shooter is still on the loose.

Law enforcement sources tell TMZ … 27-year-old Nicholas Telemaque was killed around 2:40 AM on July 4 from “multiple gunshot wounds to the upper torso.”

Minaj posted photos and messages on Twitter … saying, “Lived in Brooklyn his whole life. My precious cousin. My baby. Killed last nite.”

We’re told cops are investigating the incident — but so far, no arrests have been made.