This is gross ... a fancy private school in West Hollywood where celebs pay big bucks to educate their kids is dealing with a recent vermin infestation in its cafeteria.

The Center For Early Education was found to have pests in the areas where meals are prepared and served ... according to the Los Angeles County Department of Public Health.

Beyoncé and Jay-Z send their children to the school -- where tuition costs between $27,360 to $36,950 -- and other celeb parents include John Legend and Chrissy Teigen, Jamie Lee Curtis and Christopher Guest, Michael Eisner, Jodie Foster ... and Magic Johnson and Denzel Washington's kids have gone there, too.

The Department of Public Health closed the school's cafeteria Tuesday after a major violation regarding a vermin infestation ... which could include observations of live vermin, fresh droppings, vomit, pee stains or gnaw marks.

The Center For Early Education tells TMZ ... the kitchen was closed for 48 hours and it has since been reinspected and cleared of violations and permitted to reopen.

CEE adds ...  "As always, the health and safety of our campus and our community are of the utmost importance, and we remain ever-mindful and diligent in this regard."