Nicki Minaj to Strippers -- You Can Touch My Ass ... If I Can Touch Yours!

Nicki Minaj broke all sorts of strip club rules at a gentleman's establishment in NY last night ... when she PUT HER HANDS on the girls ... and it was awesome!!!

Minaj -- along with rappers Meek Mill and Maino -- took her big ass to Perfection Gentleman's Club in Queens last night ... where she got right up to the stage and started grinding with some of the dancers.

Before long, Nicki and the staff were feeling each other down ... with Minaj tweeting, "I love bad b*tches dats my f**kin problem."

Not a terrible problem to have ...