Madge hit the dance floor at Catch NYC late Thursday night while celebrating the birthday of her lead dancer, Loic Mabanza. She showed up after midnight with a large Gucci gift bag for Loic, and partied with the crew on the rooftop ... even when the DJ got personal by playing "Everybody."

That's usually a party faux pas, but Madonna and Loic were into it.

We're told Madonna stayed on the floor for a while -- dancing, not only to her classics, but also current hip-hop. We're told DJ Tom Macari was behind the hot playlist. Madonna also showed people pics of her daughter, Mercy James, too.

Jeezy was also in attendance, and snapped a pic with his fellow 'born legend.'