Prince Jackson -- Date with a Princess ... Allegedly

Prince Michael Jackson was out on a date with a girl who appears to be a princess ... TMZ has learned.

We got these pics of Prince and Remi Alfalah, who we're told is a Kuwaiti princess. They were bowling Wednesday at PINZ in the San Fernando Valley.

A source at the Kuwaiti consulate tells us ... Remi is indeed a princess who is a junior in high school. Michael Jackson's 16-year-old son Prince is also a junior. They attend the same private school.

Remi was dropped off at the bowling alley in a black SUV ... but he drove her home.